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On the strong cell decomposition property for weakly o‐minimal structures
Author(s) -
Wencel Roman
Publication year - 2013
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.201200016
Subject(s) - mathematics , extension (predicate logic) , equivalence relation , property (philosophy) , equivalence (formal languages) , pure mathematics , decomposition , class (philosophy) , computer science , programming language , ecology , philosophy , epistemology , artificial intelligence , biology
We consider a class of weakly o‐minimal structures admitting an o‐minimal style cell decomposition, for which one can construct certain canonical o‐minimal extension. The paper contains several fundamental facts concerning the structures in question. Among other things, it is proved that the strong cell decomposition property is preserved under elementary equivalences. We also investigate fiberwise properties (of definable sets and definable functions), definable equivalence relations, and conditions implying elimination of imaginaries.