On VC-minimal theories and variants

نویسندگان

  • Vincent Guingona
  • Michael C. Laskowski
چکیده

In this paper, we study VC-minimal theories and explore related concepts. We first define the notion of convex orderablity and show that this lies strictly between VCminimality and dp-minimality. To do this we prove a general result about set systems with independence dimension ≤ 1. 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.

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عنوان ژورنال:
  • Arch. Math. Log.

دوره 52  شماره 

صفحات  -

تاریخ انتشار 2013