منابع مشابه
Generic automorphisms and green fields
We show that the generic automorphism is axiomatizable in the green field of Poizat (once Morleyized) as well as in the bad fields that are obtained by collapsing this green field to finite Morley rank. As a corollary, we obtain ‘bad pseudofinite fields’ in characteristic 0. In both cases, we give geometric axioms. In fact, a general framework is presented allowing this kind of axiomatization. ...
متن کاملGeneric Automorphisms with prescribed Fixed Fields
This article addresses the question which structures occur as fixed structures of stable structures with a generic automorphism. Among others we give a Galois theoretic characterisation. As application we prove: Any pseudofinite field is the fixed field of some model of ACFA. Any one-free pseudo-differentially closed field of characteristic zero is the fixed field of some model of DCFA. Any one...
متن کاملMany Generic Automorphisms
Given a theory T , one may add a new unary function symbol σ to the language and add axioms to T asserting that σ is an automorphism. The model theory of generic automorphisms is the study of the model companion of the resulting theory Tσ . In this paper, we study theories equipped with more than one generic automorphism by exploring when model companions exist for such theories. In particular,...
متن کاملAutomorphisms of Finite Fields
Let F be a finite field, and 4: F* + E a surjective group homomorphism from the multiplicative group F* of F to a non-trivial abelian group E. A theorem of McConnel (Acta Arith. 8 (1963) 127-151) describes the permutations e of F with the property that d(ux uy) = d(x y) for all X, j’ E F, .Y #J. We give a short proof of this theorem, based on an argument of Bruen and Levinger (Canad. J. Math. 2...
متن کاملGeneric automorphisms and extension lemmas
Generic automorphisms are a common theme when one works with auto-morphism groups of countable structures. They play a pivotal role in reconstruction results. In these notes we shall define and explain a notion of generic, due to John Truss, which is highly relevant to reconstruction. The idea is that a generic automorphism acts on the elements of the structure in the least special way, that is...
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ژورنال
عنوان ژورنال: Annals of Pure and Applied Logic
سال: 1997
ISSN: 0168-0072
DOI: 10.1016/s0168-0072(97)00020-1