Imaginaries in Beautiful Pairs I
نویسندگان
چکیده
We prove that if T = T eq is a stable theory (without the finite cover property), then the theory TP of “beautiful pairs” eliminates imaginaries if and only if no infinite group is definable in a model of T .
منابع مشابه
Imaginaries in pairs of algebraically closed fields
We consider the theory (ACFp)P of pairs F < K of algebraically closed fields of a given characteristic p. We exhibit a collection of additional sorts in which this theory has geometric elimination of imaginaries. The sorts are essentially of the form ∪a∈B(F )Va(K)/Ga(F ), where G, V,B are varieties over the prime field G a group scheme over B and V is a scheme over B (both with irreducible fibr...
متن کاملElimination of generalised imaginaries and Galois cohomology
The objective of this article is to characterise elimination of finite generalised imaginaries as defined in [9] in terms of group cohomology. As an application, I consider series of Zariski geometries constructed [10, 23, 22] by Hrushovski and Zilber and indicate how their non-definability in algebraically closed fields is connected to eliminability of certain generalised imaginaries.
متن کاملImaginaries in Boolean algebras
Given an infinite Boolean algebra B, we find a natural class of ∅-definable equivalence relations EB such that every imaginary element from B is interdefinable with an element from a sort determined by some equivalence relation from EB . It follows that B together with the family of sorts determined by EB admits elimination of imaginaries in a suitable multisorted language. The paper generalize...
متن کاملImaginaries in Real Closed Valued Fields I
We investigate the embeddings of the value group and residue field of a real closed valued field A in Aeq via quantifier elimination in a three sorted language. We classify the one types of field elements in a real closed valued field. Finally, we investigate some of the linear structure in Aeq induced by the valuation ring V and introduce the geometric sorts. In a subsequent paper we show that...
متن کاملGroupoids, Imaginaries and Internal Covers
The questions this manuscript addresses arose in the course of an investigation of the imaginary sorts in ultraproducts of p-adic fields. These were shown to be understandable given the imaginary sorts of certain finite-dimensional vector spaces over the residue field. The residue field is pseudo-finite, and the imaginary elements there were previously studied, and shown in fact to be eliminabl...
متن کامل