Small Profinite Structures
نویسنده
چکیده
We propose a model-theoretic framework for investigating profinite structures. We prove that in many cases small profinite structures interpret infinite groups. This corresponds to results of Hrushovski and Peterzil on interpreting groups in locally modular stable and o-minimal structures.
منابع مشابه
Generalizations of small profinite structures
We generalize the model theory of small profinite structures developed by Newelski to the case of compact metric spaces considered together with compact groups of homeomorphisms.
متن کاملProfinite Structures are Retracts of Ultraproducts of Finite Structures
We establish the following model-theoretic characterization: profinite L-structures, the cofiltered limits of finite L-structures, are retracts of ultraproducts of finite L-structures. As a consequence, any elementary class of L-structures axiomatized by L-sentences of the form ∀~x(ψ0(~x) → ψ1(~x)), where ψ0(~x), ψ1(~x) are existencialpositives L-formulas, is closed under the formation of profi...
متن کاملEquational theories of profinite structures
In this paper we consider a general way of constructing profinite structures based on a given framework — a countable family of objects and a countable family of recognisers (e.g. formulas). The main theorem states: A subset of a family of recognisable sets is a lattice if and only if it is definable by a family of profinite equations. This result extends Theorem 5.2 from [GGEP08] expressed onl...
متن کاملLocally finite profinite rings
We investigate the structure of locally finite profinite rings. We classify (Jacobson-) semisimple locally finite profinite rings as products of complete matrix rings of bounded cardinality over finite fields, and we prove that the Jacobson radical of any locally finite profinite ring is nil of finite nilexponent. Our results apply to the context of small compact G-rings, where we also obtain a...
متن کاملThe Geometry of Profinite Graphs with Applications to Free Groups and Finite Monoids
We initiate the study of the class of profinite graphs Γ defined by the following geometric property: for any two vertices v and w of Γ, there is a (unique) smallest connected profinite subgraph of Γ containing them; such graphs are called tree-like. Profinite trees in the sense of Gildenhuys and Ribes are tree-like, but the converse is not true. A profinite group is then said to be dendral if ...
متن کامل