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Generalizations of small profinite structures

Published online by Cambridge University Press:  12 March 2014

Krzysztof Krupiński
Krzysztof Krupiński*
Affiliation:
Instytut Matematyczny Uniwersytetu Wrocławskiego, Pl. Grunwaldzki 2/4. 50-384 Wrocław, Poland Mathematics Department, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, IL 61801., USA. E-mail: kkrup@math.uni.wroc.pl
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Abstract

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.

Keywords

Profinite structurecompact structureindependence relation
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 75 , Issue 4 , December 2010 , pp. 1147 - 1175
Copyright
Copyright © Association for Symbolic Logic 2010

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References

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