On function field Mordell-Lang: the semiabelian case and the socle theorem

Autor: Anand Pillay, Franck Benoist, Elisabeth Bouscaren

Publikováno v: Proceedings of the London Mathematical Society
Proceedings of the London Mathematical Society, London Mathematical Society, 2018, 116 (1), pp.182-208. ⟨10.1112/plms.12076⟩

We here aim to complete our model-theoretic account of the function field Mordell-Lang conjecture, avoiding appeal to dichotomy theorems for Zariski geometries, where we now consider the general case of semiabelian varieties. The main result is a red

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Classifiable theories without finitary invariants

Autor: Ehud Hrushovski, Elisabeth Bouscaren

Publikováno v: Annals of Pure and Applied Logic. 142:296-320

It follows directly from Shelah’s structure theory that if T is a classifiable theory, then the isomorphism type of any model of T is determined by the theory of that model in the language L ∞ , ω 1 ( d . q . ) . Leo Harrington asked if one coul

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https://doi.org/10.1016/j.apal.2006.02.003

Groups definable in separably closed fields

Autor: Elisabeth Bouscaren, F. Delon

Publikováno v: Transactions of the American Mathematical Society. 354:945-966

We consider the groups which are infinitely definable in separably closed fields of finite degree of imperfection. We prove in particular that no new definable groups arise in this way: we show that any group definable in such a field L is definably

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https://doi.org/10.1090/s0002-9947-01-02886-0

S-homogeneity and automorphism groups

Autor: Michael C. Laskowski, Elisabeth Bouscaren

Publikováno v: Journal of Symbolic Logic. 58:1302-1322

We consider the question of when, given a subset A of M, the setwise stabilizer of the group of automorphisms induces a closed subgroup on Sym(A). We define s-homogeneity to be the analogue of homogeneity relative to strong embeddings and show that a

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https://doi.org/10.2307/2275145

Introduction to model theory

Autor: Elisabeth Bouscaren

Publikováno v: Lecture Notes in Mathematics ISBN: 9783540648635

In this informal presentation we introduce some of the main definitions and results which form the basis of model theory. We have chosen an approach adapted to the particular subject of this book. For proofs and formal definitions as well as for all

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https://doi.org/10.1007/978-3-540-68521-0_1