×

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.

MSC:

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

References:

[1] Transactions of the American Mathematical Society
[2] Journal of the European Mathematical Society 13 pp 1005– (2011)
[3] Canonical forms for definable subsets of algebraically closed and real closed valued fields 40 pp 843– (1995) · Zbl 0854.12003
[4] Theories controlled by formulas of Vapnik–Chervonenkis codimension (2008)
[5] Forking and independence in o-minimal theories 69 pp 215– (2004)
[6] Forking and dividing in NTP2 theories 77 pp 1– (2012)
[7] Archive for Mathematical Logic
[8] DOI: 10.1215/00294527-1435456 · Zbl 1258.03036
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.