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**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.

Reviewer: Beibut Kulpeshov (Almaty)

### MSC:

03C45 | Classification theory, stability, and related concepts in model theory |

03C64 | Model theory of ordered structures; o-minimality |

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\textit{S. Cotter} and \textit{S. Starchenko}, J. Symb. Log. 77, No. 4, 1257--1271 (2012; Zbl 1267.03046)

### 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 |

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