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Preprint Number 95

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95. Krzysztof Krupinski
Fields interpretable in rosy theories
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Submission date: 3 November 2007

Abstract:

We are working in a monster model C of a rosy theory T. We prove the following theorems, generalizing the appropriate results from the finite Morley rank case and o-minimal structures. If R is a V-definable integral domain of positive, finite thorn U-rank, then its field of fractions is interpretable in C. If A and M are infinite, definable, abelian groups such that A acts definably and faithfully on M by automorphisms, M is A-minimal and thorn U-rank of M is finite, then there is an infinite field interpretable in C. If G is an infinite, solvable but non nilpotent-by-finite, definable group of finite thorn U-rank and T has NIP, then there is an infinite field interpretable in (G, \cdot). In the last part, we show that each superrosy, dependent field K satisfies K=K^n-K^n for every n\geq 1.

Mathematics Subject Classification: 03C45, 03C60

Keywords and phrases: rosy theory, interpretable field, non independence property

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