Papers

• A note on orthogonality and stable embeddedness. With Gregory Cherlin and Marko Djordjevic. The Journal of Symbolic Logic 70 (2005), no. 4, 1359–1364.
```@article{MR2194251,
author = {Cherlin, Gregory and Djordjevic, Marko and Hrushovski, Ehud},
title = {A note on orthogonality and stable embeddedness},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {70},
year = {2005},
number = {4},
pages = {1359--1364},
issn = {0022-4812},
coden = {JSYLA6},
mrclass = {03C07 (03C45)},
mrnumber = {MR2194251}
}

```
• Model theory of endomorphisms of separably closed fields. With Zoé Chatzidakis. Journal of Algebra 281 (2004), no. 2, 567–603.
```@article{MR2098785,
author = {Chatzidakis, Zo{\'e} and Hrushovski, Ehud},
title = {Model theory of endomorphisms of separably closed fields},
journal = {J. Algebra},
fjournal = {Journal of Algebra},
volume = {281},
year = {2004},
number = {2},
pages = {567--603},
issn = {0021-8693},
coden = {JALGA4},
mrclass = {12L10 (03C60 12F10 12H10)},
mrnumber = {MR2098785 (2005h:12021)},
mrreviewer = {Dumitru Bu{\c{s}}neag}
}

```
• Generalizations of Kochen and Specker’s theorem and the effectiveness of Gleason’s theorem. With Itamar Pitowsky. Studies in History and Philosophy of Science. B. Studies in History and Philosophy of Modern Physics 35 (2004), no. 2, 177–194.
```@article{MR2075240,
author = {Hrushovski, Ehud and Pitowsky, Itamar},
title = {Generalizations of {K}ochen and {S}pecker's theorem and the effectiveness of {G}leason's theorem},
journal = {Stud. Hist. Philos. Sci. B Stud. Hist. Philos. Modern Phys.},
fjournal = {Studies in History and Philosophy of Science. B. Studies in History and Philosophy of Modern Physics},
volume = {35},
year = {2004},
number = {2},
pages = {177--194},
issn = {1355-2198},
mrclass = {81P05 (03C07 03F55 47N50 81P15)},
mrnumber = {MR2075240 (2005d:81017)},
}

```
• Perfect pseudo-algebraically closed ﬁelds are algebraically bounded. With Zoé Chatzidakis. Journal of Algebra 271 (2004), no. 2, 627–637.
```@article{MR2025543,
author = {Chatzidakis, Zo{\'e} and Hrushovski, Ehud},
title = {Perfect pseudo-algebraically closed fields are algebraically bounded},
journal = {J. Algebra},
fjournal = {Journal of Algebra},
volume = {271},
year = {2004},
number = {2},
pages = {627--637},
issn = {0021-8693},
coden = {JALGA4},
mrclass = {12L99 (03C60 12E30)},
mrnumber = {MR2025543 (2004j:12013)},
mrreviewer = {Dumitru Bu{\c{s}}neag}
}

```
• Asymptotic theories of differential fields. With Zoé Chatzidakis. Illinois Journal of Mathematics 47 (2003), no. 3, 593–618.
```@article{MR2007226,
author = {Chatzidakis, Zo{\'e} and Hrushovski, Ehud},
title = {Asymptotic theories of differential fields},
journal = {Illinois J. Math.},
fjournal = {Illinois Journal of Mathematics},
volume = {47},
year = {2003},
number = {3},
pages = {593--618},
issn = {0019-2082},
coden = {IJMTAW},
mrclass = {12L12 (03C60 12H99)},
mrnumber = {MR2007226 (2004i:12011)},
mrreviewer = {Zbigniew Hajto}
}

```
• On model complete differential fields. With M. Itai. Transactions of the American Mathematical Society 355 (2003), no. 11, 4267–4296 (electronic).
```@article{MR1990753,
author = {Hrushovski, E. and Itai, M.},
title = {On model complete differential fields},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {355},
year = {2003},
number = {11},
pages = {4267--4296 (electronic)},
issn = {0002-9947},
coden = {TAMTAM},
mrclass = {03C60 (12H05)},
mrnumber = {MR1990753 (2004m:03139)},
mrreviewer = {Wai Yan Pong}
}

```
• Interpretable groups, stably embedded sets, and Vaughtian pairs. With Bernhard Herwig and Dugald Macpherson. Journal of the London Mathematical Society. Second Series 68 (2003), no. 1, 1–11.
```@article{MR1980239,
author = {Herwig, Bernhard and Hrushovski, Ehud and Macpherson, Dugald},
title = {Interpretable groups, stably embedded sets, and {V}aughtian pairs},
journal = {J. London Math. Soc. (2)},
fjournal = {Journal of the London Mathematical Society. Second Series},
volume = {68},
year = {2003},
number = {1},
pages = {1--11},
issn = {0024-6107},
coden = {JLMSAK},
mrclass = {03C52 (03C45 03C95)},
mrnumber = {MR1980239 (2004c:03045)},
mrreviewer = {Eric Jaligot}
}

```
• Finite structures with few types. With Gregory Cherlin. Annals of Mathematics Studies, Princeton University Press, Princeton, NJ, 2003.
```@book{MR1961194,
author = {Cherlin, Gregory and Hrushovski, Ehud},
title = {Finite structures with few types},
series = {Annals of Mathematics Studies},
volume = {152},
publisher = {Princeton University Press},
year = {2003},
pages = {vi+193},
isbn = {0-691-11331-9; 0-691-11332-7},
mrclass = {03C13 (03-02 03C45 03C50 03C60 20A15)},
mrnumber = {MR1961194 (2004c:03037)},
mrreviewer = {H. Dugald Macpherson}
}

```
• Pseudo-ﬁnite ﬁelds and related structures. Model theory and applications, Quad. Mat., vol. 11, Aracne, Rome, , 2002, pp. 151–212.
```@incollection{MR2159717,
author = {Hrushovski, Ehud},
title = {Pseudo-finite fields and related structures},
booktitle = {Model theory and applications},
volume = {11},
pages = {151--212},
publisher = {Aracne, Rome},
year = {2002},
mrclass = {03C60 (03C45 12F10)},
mrnumber = {MR2159717 (2006d:03059)},
mrreviewer = {H. Dugald Macpherson}
}

```
• Computing the Galois group of a linear differential equation. Differential Galois theory (Bedlewo, 2001), Banach Center Publ., vol. 58, Polish Acad. Sci., Warsaw, 2002, pp. 97–138.
```@incollection{MR1972449,
author = {Hrushovski, Ehud},
title = {Computing the {G}alois group of a linear differential equation},
booktitle = {Differential Galois theory (B\polhk edlewo, 2001)},
series = {Banach Center Publ.},
volume = {58},
pages = {97--138},
year = {2002},
mrclass = {12H05 (03C60 12L05 34A30)},
mrnumber = {MR1972449 (2004j:12007)},
mrreviewer = {{\c{S}}. A. Basarab}
}

```
• Model theory of difference ﬁelds. II. Periodic ideals and the trichotomy in all characteristics. With Zoé Chatzidakis and Ya’acov Peterzil. Proceedings of the London Mathematical Society. Third Series 85 (2002), no. 2, 257–311.
```@article{MR1912052,
author = {Chatzidakis, Zo{\'e} and Hrushovski, Ehud and Peterzil, Ya'acov},
title = {Model theory of difference fields. {II}. {P}eriodic ideals and the trichotomy in all characteristics},
journal = {Proc. London Math. Soc. (3)},
fjournal = {Proceedings of the London Mathematical Society. Third Series},
volume = {85},
year = {2002},
number = {2},
pages = {257--311},
issn = {0024-6115},
coden = {PLMTAL},
mrclass = {03C60 (03C45 08A35 12H05)},
mrnumber = {MR1912052 (2004c:03047)},
mrreviewer = {Carlo Toffalori}
}

```
• Unique decomposition in classifiable theories. With Bradd Hart and Michael C. Laskowski. The Journal of Symbolic Logic 67 (2002), no. 1, 61–68.
```@article{MR1889536,
title = {Unique decomposition in classifiable theories},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {67},
year = {2002},
number = {1},
pages = {61--68},
issn = {0022-4812},
coden = {JSYLA6},
mrclass = {03C45},
mrnumber = {MR1889536 (2003g:03056)},
mrreviewer = {Bernhard F. Herwig}
}

```
• La limite des théories de courbes génériques. With Olivier Chapuis, Pascal Koiran and Bruno Poizat. The Journal of Symbolic Logic 67 (2002), no. 1, 24–34.
```@article{MR1889534,
author = {Chapuis, Olivier and Hrushovski, Ehud and Koiran, Pascal and Poizat, Bruno},
title = {La limite des th\'eories de courbes g\'en\'eriques},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {67},
year = {2002},
number = {1},
pages = {24--34},
issn = {0022-4812},
coden = {JSYLA6},
mrclass = {03C60 (13L05)},
mrnumber = {MR1889534 (2003a:03051)},
mrreviewer = {Yehuda Rav}
}

```
• The Manin-Mumford conjecture and the model theory of difference ﬁelds. Annals of Pure and Applied Logic 112 (2001), no. 1, 43–115.
```@article{MR1854232,
author = {Hrushovski, Ehud},
title = {The {M}anin-{M}umford conjecture and the model theory of difference fields},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {112},
year = {2001},
number = {1},
pages = {43--115},
issn = {0168-0072},
coden = {APALD7},
mrclass = {03C60 (11G10 11U09 12L12)},
mrnumber = {MR1854232 (2003d:03061)},
mrreviewer = {C. Toffalori}
}

```
• The uncountable spectra of countable theories. With Bradd Hart and Michael C. Laskowski. Annals of Mathematics. Second Series 152 (2000), no. 1, 207–257.
```@article{MR1792295,
title = {The uncountable spectra of countable theories},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {152},
year = {2000},
number = {1},
pages = {207--257},
issn = {0003-486X},
coden = {ANMAAH},
mrclass = {03C45},
mrnumber = {MR1792295 (2002a:03063)},
mrreviewer = {John T. Baldwin},
eprint = {arXiv:math.LO/0007199}
}

```
• Effective bounds for the number of transcendental points on subvarieties of semi-abelian varieties. With Anand Pillay. American Journal of Mathematics 122 (2000), no. 3, 439–450.
```@article{MR1759883,
author = {Hrushovski, Ehud and Pillay, Anand},
title = {Effective bounds for the number of transcendental points on subvarieties of semi-abelian varieties},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {122},
year = {2000},
number = {3},
pages = {439--450},
issn = {0002-9327},
coden = {AJMAAN},
mrclass = {11J95 (14K15)},
mrnumber = {MR1759883 (2001d:11078)},
mrreviewer = {Danielle Gondard-Cozette}
}

```
• Lascar and Morley ranks differ in differentially closed ﬁelds. With Thomas Scanlon. The Journal of Symbolic Logic 64 (1999), no. 3, 1280–1284.
```@article{MR1779761,
author = {Hrushovski, Ehud and Scanlon, Thomas},
title = {Lascar and {M}orley ranks differ in differentially closed fields},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {64},
year = {1999},
number = {3},
pages = {1280--1284},
issn = {0022-4812},
coden = {JSYLA6},
mrclass = {03C60 (03C45 12H05)},
mrnumber = {MR1779761 (2002g:03082)},
mrreviewer = {Carlo Toffalori},
eprint = {arXiv:math.RA/9809190}
}

```
• Model theory of difference fields. With Zoé Chatzidakis. Transactions of the American Mathematical Society 351 (1999), no. 8, 2997–3071.
```@article{MR1652269,
author = {Chatzidakis, Zo{\'e} and Hrushovski, Ehud},
title = {Model theory of difference fields},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {351},
year = {1999},
number = {8},
pages = {2997--3071},
issn = {0002-9947},
coden = {TAMTAM},
mrclass = {03C60 (03C45 08A35 12L12)},
mrnumber = {MR1652269 (2000f:03109)},
mrreviewer = {Salma Kuhlmann}
}

```
• Proof of Manin’s theorem by reduction to positive characteristic. Model theory and algebraic geometry, Lecture Notes in Math., vol. 1696, Springer, Berlin, 1998, pp. 197–205.
```@incollection{MR1678551,
author = {Hrushovski, Ehud},
title = {Proof of {M}anin's theorem by reduction to positive characteristic},
booktitle = {Model theory and algebraic geometry},
series = {Lecture Notes in Math.},
volume = {1696},
pages = {197--205},
publisher = {Springer},
year = {1998},
mrclass = {11U09 (11G10)},
mrnumber = {MR1678551 (2000c:11202)},
mrreviewer = {Alexandru Buium}
}

```
• Linear ultrafilters. With George M. Bergman. Communications in Algebra 26 (1998), no. 12, 4079–4113.
```@article{MR1661256,
author = {Bergman, George M. and Hrushovski, Ehud},
title = {Linear ultrafilters},
journal = {Comm. Algebra},
fjournal = {Communications in Algebra},
volume = {26},
year = {1998},
number = {12},
pages = {4079--4113},
issn = {0092-7872},
coden = {COALDM},
mrclass = {03C20 (03C60 12L10 16K40)},
mrnumber = {MR1661256 (2000c:03025)},
mrreviewer = {M. Yasuhara}
}

```
• Geometric model theory. Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998), 281–302 (electronic), 1998, .
```@inproceedings{MR1648035,
author = {Hrushovski, Ehud},
title = {Geometric model theory},
booktitle = {Proceedings of the International Congress of Mathematicians, Vol. I (Berlin, 1998)},
journal = {Doc. Math.},
fjournal = {Documenta Mathematica},
year = {1998},
number = {Extra Vol. I},
pages = {281--302 (electronic)},
issn = {1431-0635},
mrclass = {03C45 (03C60 11U09 14G99)},
mrnumber = {MR1648035 (2000b:03120)},
}

```
• Stability and its uses. Current developments in mathematics, 1996 (Cambridge, MA), , vol. , Int. Press, Boston, MA, , 1997, pp. 61–103.
```@incollection{MR1724945,
author = {Hrushovski, Ehud},
title = {Stability and its uses},
booktitle = {Current developments in mathematics, 1996 (Cambridge, MA)},
pages = {61--103},
publisher = {Int. Press, Boston, MA},
year = {1997},
mrclass = {11U09 (03C45 03C60 11G35)},
mrnumber = {MR1724945 (2000h:11124)},
mrreviewer = {Anand Pillay}
}

```
• The Mordell-Lang conjecture for function ﬁelds. Journal of the American Mathematical Society 9 (1996), no. 3, 667–690.
```@article{MR1333294,
author = {Hrushovski, Ehud},
title = {The {M}ordell-{L}ang conjecture for function fields},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {9},
year = {1996},
number = {3},
pages = {667--690},
issn = {0894-0347},
mrclass = {11U09 (03C60 11G10 14G99)},
mrnumber = {MR1333294 (97h:11154)},
mrreviewer = {Anand Pillay}
}

```
• Powers in finitely generated groups. With P. H. Kropholler, A. Lubotzky and A. Shalev. Transactions of the American Mathematical Society 348 (1996), no. 1, 291–304.
```@article{MR1316851,
author = {Hrushovski, E. and Kropholler, P. H. and Lubotzky, A. and Shalev, A.},
title = {Powers in finitely generated groups},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {348},
year = {1996},
number = {1},
pages = {291--304},
issn = {0002-9947},
coden = {TAMTAM},
mrclass = {20F99},
mrnumber = {MR1316851 (96f:20061)},
mrreviewer = {D. J. S. Robinson}
}

```
• Zariski geometries. With Boris Zilber. Journal of the American Mathematical Society 9 (1996), no. 1, 1–56.
```@article{MR1311822,
author = {Hrushovski, Ehud and Zilber, Boris},
title = {Zariski geometries},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {9},
year = {1996},
number = {1},
pages = {1--56},
issn = {0894-0347},
mrclass = {03C60 (03C45 14A10 14H99)},
mrnumber = {MR1311822 (96c:03077)},
mrreviewer = {G. Cherlin}
}

```
• The automorphism group of the combinatorial geometry of an algebraically closed field. With David M. Evans. Journal of the London Mathematical Society. Second Series 52 (1995), no. 2, 209–225.
```@article{MR1356137,
author = {Evans, David M. and Hrushovski, Ehud},
title = {The automorphism group of the combinatorial geometry of an algebraically closed field},
journal = {J. London Math. Soc. (2)},
fjournal = {Journal of the London Mathematical Society. Second Series},
volume = {52},
year = {1995},
number = {2},
pages = {209--225},
issn = {0024-6107},
coden = {JLMSAK},
mrclass = {51D20 (03C60)},
mrnumber = {MR1356137 (97f:51012)},
mrreviewer = {Anand Pillay}
}

```
• Definable subgroups of algebraic groups over finite fields. With A. Pillay. Journal für die Reine und Angewandte Mathematik 462 (1995), 69–91.
```@article{MR1329903,
author = {Hrushovski, E. and Pillay, A.},
title = {Definable subgroups of algebraic groups over finite fields},
journal = {J. Reine Angew. Math.},
fjournal = {Journal f{\"u}r die Reine und Angewandte Mathematik},
volume = {462},
year = {1995},
pages = {69--91},
issn = {0075-4102},
coden = {JRMAA8},
mrclass = {20G40 (03C40 03C45 03C60 20A15)},
mrnumber = {MR1329903 (97f:20059)},
mrreviewer = {Lou van den Dries}
}

```
• Singular compactness and the Neveu decomposition. With G. Grabarnik. Israel Journal of Mathematics 89 (1995), no. 1-3, 135–139.
```@article{MR1324457,
author = {Grabarnik, G. and Hrushovski, E.},
title = {Singular compactness and the {N}eveu decomposition},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {89},
year = {1995},
number = {1-3},
pages = {135--139},
issn = {0021-2172},
coden = {ISJMAP},
mrclass = {28D15},
mrnumber = {MR1324457 (96f:28023)},
mrreviewer = {A. Precupanu}
}

```
• Finitely axiomatizable ${\aleph }_{1}$ categorical theories. The Journal of Symbolic Logic 59 (1994), no. 3, 838–844.
```@article{MR1295972,
author = {Hrushovski, Ehud},
title = {Finitely axiomatizable {\$\aleph\sb 1\$} categorical theories},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {59},
year = {1994},
number = {3},
pages = {838--844},
issn = {0022-4812},
coden = {JSYLA6},
mrclass = {03C35 (03C45)},
mrnumber = {MR1295972 (95k:03061)},
mrreviewer = {John T. Baldwin}
}

```
• On one-based theories. With E. Bouscaren. The Journal of Symbolic Logic 59 (1994), no. 2, 579–595.
```@article{MR1276634,
author = {Bouscaren, E. and Hrushovski, E.},
title = {On one-based theories},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {59},
year = {1994},
number = {2},
pages = {579--595},
issn = {0022-4812},
coden = {JSYLA6},
mrclass = {03C45},
mrnumber = {MR1276634 (95e:03103)},
mrreviewer = {Anand Pillay}
}

```
• Groups deﬁnable in local ﬁelds and pseudo-ﬁnite ﬁelds. With Anand Pillay. Israel Journal of Mathematics 85 (1994), no. 1-3, 203–262.
```@article{MR1264346,
author = {Hrushovski, Ehud and Pillay, Anand},
title = {Groups definable in local fields and pseudo-finite fields},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {85},
year = {1994},
number = {1-3},
pages = {203--262},
issn = {0021-2172},
coden = {ISJMAP},
mrclass = {12L12 (03C40 03C45 03C60)},
mrnumber = {MR1264346 (95f:12015)},
mrreviewer = {Luc B{\'e}lair}
}

```
• A non-PAC ﬁeld whose maximal purely inseparable extension is PAC. Israel Journal of Mathematics 85 (1994), no. 1-3, 199–202.
```@article{MR1264345,
author = {Hrushovski, Ehud},
title = {A non-{PAC} field whose maximal purely inseparable extension is {PAC}},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {85},
year = {1994},
number = {1-3},
pages = {199--202},
issn = {0021-2172},
coden = {ISJMAP},
mrclass = {12F15},
mrnumber = {MR1264345 (95a:12010)},
mrreviewer = {John Swallow}
}

```
• Finite structures with few types. Finite and infinite combinatorics in sets and logic (Banff, AB, 1991), NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 411, Kluwer Acad. Publ., Dordrecht, 1993, pp. 175–187.
```@incollection{MR1261204,
author = {Hrushovski, Ehud},
title = {Finite structures with few types},
booktitle = {Finite and infinite combinatorics in sets and logic (Banff, AB, 1991)},
series = {NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci.},
volume = {411},
pages = {175--187},
year = {1993},
mrclass = {03C45 (03C13)},
mrnumber = {MR1261204 (95h:03084)},
}

```
• A new strongly minimal set. Annals of Pure and Applied Logic 62 (1993), no. 2, 147–166.
```@article{MR1226304,
author = {Hrushovski, Ehud},
title = {A new strongly minimal set},
note = {Stability in model theory, III (Trento, 1991)},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {62},
year = {1993},
number = {2},
pages = {147--166},
issn = {0168-0072},
coden = {APALD7},
mrclass = {03C45 (03C35)},
mrnumber = {MR1226304 (94d:03064)},
mrreviewer = {Alexandre Ivanov}
}

```
• On the automorphism groups of finite covers. With David M. Evans. Annals of Pure and Applied Logic 62 (1993), no. 2, 83–112.
```@article{MR1226301,
author = {Evans, David M. and Hrushovski, Ehud},
title = {On the automorphism groups of finite covers},
note = {Stability in model theory, III (Trento, 1991)},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {62},
year = {1993},
number = {2},
pages = {83--112},
issn = {0168-0072},
coden = {APALD7},
mrclass = {03C45 (20B27)},
mrnumber = {MR1226301 (94e:03035)},
}

```
• Zariski geometries. With Boris Zilber. American Mathematical Society. Bulletin. New Series 28 (1993), no. 2, 315–323.
```@article{MR1183999,
author = {Hrushovski, Ehud and Zilber, Boris},
title = {Zariski geometries},
journal = {Bull. Amer. Math. Soc. (N.S.)},
fjournal = {American Mathematical Society. Bulletin. New Series},
volume = {28},
year = {1993},
number = {2},
pages = {315--323},
issn = {0273-0979},
mrclass = {14A99 (03C45 03C60 03C65 14H99)},
mrnumber = {MR1183999 (93j:14003)},
mrreviewer = {Liam O'Carroll},
eprint = {arXiv:math.AG/9304212}
}

```
• Strongly minimal expansions of algebraically closed fields. Israel Journal of Mathematics 79 (1992), no. 2-3, 129–151.
```@article{MR1248909,
author = {Hrushovski, Ehud},
title = {Strongly minimal expansions of algebraically closed fields},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {79},
year = {1992},
number = {2-3},
pages = {129--151},
issn = {0021-2172},
coden = {ISJMAP},
mrclass = {03C45 (03C35 03C60 12L12)},
mrnumber = {MR1248909 (95c:03078)},
mrreviewer = {U. Felgner}
}

```
• Extending partial isomorphisms of graphs. Combinatorica. An International Journal on Combinatorics and the Theory of Computing 12 (1992), no. 4, 411–416.
```@article{MR1194731,
author = {Hrushovski, Ehud},
title = {Extending partial isomorphisms of graphs},
journal = {Combinatorica},
fjournal = {Combinatorica. An International Journal on Combinatorics and the Theory of Computing},
volume = {12},
year = {1992},
number = {4},
pages = {411--416},
issn = {0209-9683},
coden = {COMBDI},
mrclass = {05C25 (05C80)},
mrnumber = {MR1194731 (93m:05089)},
mrreviewer = {Martin {\v{S}}koviera}
}

```
• Unimodular minimal structures. Journal of the London Mathematical Society. Second Series 46 (1992), no. 3, 385–396.
```@article{MR1190425,
author = {Hrushovski, Ehud},
title = {Unimodular minimal structures},
journal = {J. London Math. Soc. (2)},
fjournal = {Journal of the London Mathematical Society. Second Series},
volume = {46},
year = {1992},
number = {3},
pages = {385--396},
issn = {0024-6107},
coden = {JLMSAK},
mrclass = {03C45 (03C60)},
mrnumber = {MR1190425 (94b:03062)},
mrreviewer = {John T. Baldwin}
}

```
• Stability and omitting types. With Saharon Shelah. Israel Journal of Mathematics 74 (1991), no. 2-3, 289–321.
```@article{MR1135241,
author = {Hrushovski, Ehud and Shelah, Saharon},
title = {Stability and omitting types},
journal = {Israel J. Math.},
fjournal = {Israel Journal of Mathematics},
volume = {74},
year = {1991},
number = {2-3},
pages = {289--321},
issn = {0021-2172},
coden = {ISJMAP},
mrclass = {03C45},
mrnumber = {MR1135241 (92m:03049)},
mrreviewer = {G. Cherlin}
}

```
• Projective planes in algebraically closed fields. With David M. Evans. Proceedings of the London Mathematical Society. Third Series 62 (1991), no. 1, 1–24.
```@article{MR1078211,
author = {Evans, David M. and Hrushovski, Ehud},
title = {Projective planes in algebraically closed fields},
journal = {Proc. London Math. Soc. (3)},
fjournal = {Proceedings of the London Mathematical Society. Third Series},
volume = {62},
year = {1991},
number = {1},
pages = {1--24},
issn = {0024-6115},
coden = {PLMTAL},
mrclass = {05B25 (03C45 03C60 03D35 05B35 51E12)},
mrnumber = {MR1078211 (92a:05031)},
mrreviewer = {Daniel Lascar}
}

```
• Unidimensional theories are superstable. Annals of Pure and Applied Logic 50 (1990), no. 2, 117–138.
```@article{MR1081816,
author = {Hrushovski, Ehud},
title = {Unidimensional theories are superstable},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {50},
year = {1990},
number = {2},
pages = {117--138},
issn = {0168-0072},
coden = {APALD7},
mrclass = {03C45 (03C60)},
mrnumber = {MR1081816 (92g:03052)},
}

```
• Classiﬁcation theory, $n$-tuples of models and ﬁnite determinacy. With Elisabeth Bouscaren. Proceedings of the 7th Easter Conference on Model Theory (Wendisch-Rietz, 1989) , 58–66, Seminarberichte, 104, Humboldt Univ. Berlin, 1989, .
```@inproceedings{MR1045012,
author = {Bouscaren, Elisabeth and Hrushovski, Ehud},
title = {Classification theory, {\$n\$}-tuples of models and finite determinacy},
booktitle = {Proceedings of the 7th Easter Conference on Model Theory (Wendisch-Rietz, 1989)},
series = {Seminarberichte},
volume = {104},
pages = {58--66},
publisher = {Humboldt Univ. Berlin},
year = {1989},
mrclass = {03C45},
mrnumber = {MR1045012 (90m:03066)}
}

```
• A dichotomy theorem for regular types. With Saharon Shelah. Annals of Pure and Applied Logic 45 (1989), no. 2, 157–169.
```@article{MR1044122,
author = {Hrushovski, Ehud and Shelah, Saharon},
title = {A dichotomy theorem for regular types},
note = {Stability in model theory, II (Trento, 1987)},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {45},
year = {1989},
number = {2},
pages = {157--169},
issn = {0168-0072},
coden = {APALD7},
mrclass = {03C45},
mrnumber = {MR1044122 (91g:03068)},
mrreviewer = {John T. Baldwin}
}

```
• Almost orthogonal regular types. Annals of Pure and Applied Logic 45 (1989), no. 2, 139–155.
```@article{MR1044121,
author = {Hrushovski, Ehud},
title = {Almost orthogonal regular types},
note = {Stability in model theory, II (Trento, 1987)},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {45},
year = {1989},
number = {2},
pages = {139--155},
issn = {0168-0072},
coden = {APALD7},
mrclass = {03C45 (20A15)},
mrnumber = {MR1044121 (91k:03083)},
mrreviewer = {W. Hodges}
}

```
• Unidimensional theories. An introduction to geometric stability theory. Logic Colloquium ’87 (Granada, 1987), Stud. Logic Found. Math., vol. 129, North-Holland, Amsterdam, 1989, pp. 73–103.
```@incollection{MR1015305,
author = {Hrushovski, Ehud},
title = {Unidimensional theories. {A}n introduction to geometric stability theory},
booktitle = {Logic Colloquium '87 (Granada, 1987)},
series = {Stud. Logic Found. Math.},
volume = {129},
pages = {73--103},
publisher = {North-Holland},
year = {1989},
mrclass = {03C45},
mrnumber = {MR1015305 (90j:03061)},
mrreviewer = {Bruno Poizat}
}

```
• Finitely based theories. The Journal of Symbolic Logic 54 (1989), no. 1, 221–225.
```@article{MR987333,
author = {Hrushovski, Ehud},
title = {Finitely based theories},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {54},
year = {1989},
number = {1},
pages = {221--225},
issn = {0022-4812},
coden = {JSYLA6},
mrclass = {03C45},
mrnumber = {MR987333 (90a:03041)},
mrreviewer = {John T. Baldwin}
}

```
• Kueker’s conjecture for stable theories. The Journal of Symbolic Logic 54 (1989), no. 1, 207–220.
```@article{MR987332,
author = {Hrushovski, Ehud},
title = {Kueker's conjecture for stable theories},
journal = {J. Symbolic Logic},
fjournal = {The Journal of Symbolic Logic},
volume = {54},
year = {1989},
number = {1},
pages = {207--220},
issn = {0022-4812},
coden = {JSYLA6},
mrclass = {03C45},
mrnumber = {MR987332 (90b:03046)},
mrreviewer = {Chantal Berline}
}

```
• On superstable fields with automorphisms. The model theory of groups (Notre Dame, IN, 1985–1987), Notre Dame Math. Lectures, vol. 11, Univ. Notre Dame Press, Notre Dame, IN, 1989, pp. 186–191.
```@incollection{MR985346,
author = {Hrushovski, Ehud},
title = {On superstable fields with automorphisms},
booktitle = {The model theory of groups (Notre Dame, IN, 1985--1987)},
series = {Notre Dame Math. Lectures},
volume = {11},
pages = {186--191},
publisher = {Univ. Notre Dame Press},
year = {1989},
mrclass = {03C45 (03C60 12L12)},
mrnumber = {MR985346}
}

```
• Totally categorical structures. Transactions of the American Mathematical Society 313 (1989), no. 1, 131–159.
```@article{MR943605,
author = {Hrushovski, Ehud},
title = {Totally categorical structures},
journal = {Trans. Amer. Math. Soc.},
fjournal = {Transactions of the American Mathematical Society},
volume = {313},
year = {1989},
number = {1},
pages = {131--159},
issn = {0002-9947},
coden = {TAMTAM},
mrclass = {03C45 (03C35)},
mrnumber = {MR943605 (90f:03064)},
mrreviewer = {U. Felgner}
}

```
• Locally modular regular types. Classification theory (Chicago, IL, 1985), Lecture Notes in Math., vol. 1292, Springer, Berlin, 1987, pp. 132–164.
```@incollection{MR1033027,
author = {Hrushovski, Ehud},
title = {Locally modular regular types},
booktitle = {Classification theory (Chicago, IL, 1985)},
series = {Lecture Notes in Math.},
volume = {1292},
pages = {132--164},
publisher = {Springer},
year = {1987},
mrclass = {03C45 (20K99)},
mrnumber = {MR1033027 (90m:03064)},
mrreviewer = {Anand Pillay}
}

```
• Weakly normal groups. With A. Pillay. Logic colloquium ’85 (Orsay, 1985), Stud. Logic Found. Math., vol. 122, North-Holland, Amsterdam, 1987, pp. 233–244.
```@incollection{MR895647,
author = {Hrushovski, U. and Pillay, A.},
title = {Weakly normal groups},
booktitle = {Logic colloquium '85 (Orsay, 1985)},
series = {Stud. Logic Found. Math.},
volume = {122},
pages = {233--244},
publisher = {North-Holland},
year = {1987},
mrclass = {03C45 (03C60 20A15)},
mrnumber = {MR895647 (88e:03051)},
}

```
• Identities of cofinal sublattices. With George M. Bergman. Order 2 (1985), no. 2, 173–191.
```@article{MR815863,
author = {Bergman, George M. and Hrushovski, Ehud},
title = {Identities of cofinal sublattices},
journal = {Order},
fjournal = {Order},
volume = {2},
year = {1985},
number = {2},
pages = {173--191},
issn = {0167-8094},
coden = {ORDRE5},
mrclass = {06C05 (06B20 16A33)},
mrnumber = {MR815863 (87k:06020)},
mrreviewer = {S. Comer}
}

```
• The Elementary Theory of the Frobenius Automorphisms.

A Frobenius difference ﬁeld is an algebraically closed ﬁeld of characteristic $p>0$, enriched with a symbol for $x↦{x}^{{p}^{m}}$. We study a sentence or formula in the language of ﬁelds with a distinguished automorphism, interpreted in Frobenius difference ﬁelds with $p$ or $m$ tending to inﬁnity. In particular, a decision procedure is found to determine when a sentence is true in almost every Frobenius difference ﬁeld. This generalizes Cebotarev’s density theorem and Weil’s Riemann hypothesis for curves (both in qualitative versions), but hinges on a result going slightly beyond the latter.

The setting for the proof is the geometry of difference varieties of transformal dimension zero; these generalize algebraic varieties, and are shown to have a rich structure, only partly explicated here.

Some applications are given, in particular to ﬁnite simple groups, and to the Jacobi bound for difference equations.

```@misc{math.LO/0406514,
title = {{The Elementary Theory of the Frobenius Automorphisms}},
author = {Ehud Hrushovski},
eprint = {arXiv:math.LO/0406514}
}

```
• Integration in valued ﬁelds. With David Kazhdan.

We develop a theory of integration over valued ﬁelds of residue characteristic zero. In particular we obtain new and base-ﬁeld independent foundations for integration over local ﬁelds of large residue characteristic, extending results of Denef,Loeser, Cluckers. The method depends on an analysis of deﬁnable sets up to deﬁnable bijections. We obtain a precise description of the Grothendieck semigroup of such sets in terms of related groups over the residue ﬁeld and value group. This yields new invariants of all deﬁnable bijections, as well as invariants of measure preserving bijections.

```@misc{math.AG/0510133,
title = {{Integration in valued fields}},
author = {Ehud Hrushovski and David Kazhdan},
eprint = {arXiv:math.AG/0510133}
}

```

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