On VC-density in VC-minimal theories

2014/09/29 by Guingona, Vincent
#03C45 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1409.8060

Abstract

We show that any formula with two free variables in a VC-minimal theory has VC-codensity at most two. Modifying the argument slightly, we give a new proof of the fact that, in a VC-minimal theory where acl = dcl, the VC-codensity of a formula is at most the number of free variables.

Related

• On VC-minimal theories and variants
• Vapnik-Chervonenkis density in some theories without the independence property, I
• VC-Density in Pairs of Ordered Vector Space
• A note on uniform definability of types over finite sets in partial orders of finite width
• Forcing of infinity and algebras of distributions of binary\n semi-isolating formulas for strongly minimal theories