Journal of Symbolic Logic 75 (4):1147-1175 (2010)

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 structure   compact structure   independence relation
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DOI 10.2178/jsl/1286198141
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References found in this work BETA

Galois Groups of First Order Theories.E. Casanovas, D. Lascar, A. Pillay & M. Ziegler - 2001 - Journal of Mathematical Logic 1 (02):305-319.
A Note on Lascar Strong Types in Simple Theories.Byunghan Kim - 1998 - Journal of Symbolic Logic 63 (3):926-936.
On Bounded Type-Definable Equivalence Relations.Ludomir Newelski & Krzysztof Krupi?Ski - 2002 - Notre Dame Journal of Formal Logic 43 (4):231-242.
Hyperimaginaries and Automorphism Groups.D. Lascar & A. Pillay - 2001 - Journal of Symbolic Logic 66 (1):127-143.
Flat Morley Sequences.Ludomir Newelski - 1999 - Journal of Symbolic Logic 64 (3):1261-1279.

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Citations of this work BETA

Geometric Stability Theory for Μ-Structures.Junguk Lee - 2019 - Annals of Pure and Applied Logic 170 (8):843-866.
Definable Topological Dynamics.Krzysztof Krupiński - 2017 - Journal of Symbolic Logic 82 (3):1080-1105.

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