On Finite Imaginaries
نویسنده
چکیده
We study finite imaginaries in certain valued fields, and prove a conjecture of Cluckers and Denef.
منابع مشابه
Groupoids, 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 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 Beautiful Pairs I
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 .
متن کاملDefinable Operations on Sets and Elimination of Imaginaries
This paper gives a new and constructive proof of Poizat's theorem that the theory of algebraically closed fields admits elimination of imaginaries. The proof uses ideas of definability for properties and operations on definable sets. In addition, the property of being finite in an algebrically closed field, as well as the property of having a given algebraic dimension are shown to be definable ...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009