105 research outputs found
Fields and Fusions: Hrushovski constructions and their definable groups
An overview is given of the various expansions of fields and fusions of
strongly minimal sets obtained by means of Hrushovski's amalgamation method, as
well as a characterization of the groups definable in these structures
The theory of the exponential differential equations of semiabelian varieties
The complete first order theories of the exponential differential equations
of semiabelian varieties are given. It is shown that these theories also arises
from an amalgamation-with-predimension construction in the style of Hrushovski.
The theory includes necessary and sufficient conditions for a system of
equations to have a solution. The necessary condition generalizes Ax's
differential fields version of Schanuel's conjecture to semiabelian varieties.
There is a purely algebraic corollary, the "Weak CIT" for semiabelian
varieties, which concerns the intersections of algebraic subgroups with
algebraic varieties.Comment: 53 pages; v3: Substantial changes, including a completely new
introductio
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Model Theory: Around Valued Fields and Dependent Theories
The general topic of the meeting was “Valued fields and related structures”. It included both applications of model theory, as well as so-called “pure” model theory: the classification of first order structures using new techniques extending those developed in stable theories
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