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Preprint Number 364

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364. Vincent Guingona, Michael C. Laskowski
On VC-minimal theories and variants
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Submission date: 20 October 2011.

Abstract:

In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablility and show that this lies strictly between VC-minimality and dp-minimality. Next, we define the notion of weak VC-minimality, show it lies strictly between VC-minimality and dependence, and show that all unstable weakly VC-minimal theories interpret an infinite linear order. Finally, we define the notion full VC-minimality, show that this lies strictly between weak o-minimality and VC-minimality, and show that theories that are fully VC-minimal have low VC-density.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 1110.4274: pdf, ps.


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