December 2010 Generalizations of small profinite structures
Krzysztof Krupiński
J. Symbolic Logic 75(4): 1147-1175 (December 2010). DOI: 10.2178/jsl/1286198141


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 and satisfying the existence of m-independent extensions (we call them compact e-structures). We analyze the relationships between smallness and different versions of the assumption of the existence of m-independent extensions and we obtain some topological consequences of these assumptions. Using them, we adopt Newelski's proofs of various results about small profinite structures to compact e-structures. In particular, we notice that a variant of the group configuration theorem holds in this context. A general construction of compact structures is described. Using it, a class of examples of compact e-structures which are not small is constructed. It is also noticed that in an m-stable compact e-structure every orbit is equidominant with a product of m-regular orbits. %which is new even for small profinite structures.


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Krzysztof Krupiński. "Generalizations of small profinite structures." J. Symbolic Logic 75 (4) 1147 - 1175, December 2010.


Published: December 2010
First available in Project Euclid: 4 October 2010

zbMATH: 1219.03037
MathSciNet: MR2767962
Digital Object Identifier: 10.2178/jsl/1286198141

Primary: 03C45 , 54H99

Keywords: compact structure , independence relation , Profinite structure

Rights: Copyright © 2010 Association for Symbolic Logic


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Vol.75 • No. 4 • December 2010
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