Forking in VC-minimal theories. (English) Zbl 1267.03046

The authors consider the notion of VC-minimality, firstly introduced by H. Adler, and being a generalization of the following notions: strong minimality, weak o-minimality and C-minimality. The main result of the paper is to find some equivalent conditions for forking of formulae over models in VC-minimal theories that generalizes a result by A. Dolich on o-minimal theories. Also, some basic results concerning VC-minimality and decompositions of definable sets in VC-minimal theories are presented.


03C45 Classification theory, stability, and related concepts in model theory
03C64 Model theory of ordered structures; o-minimality
Full Text: DOI Euclid


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