Theories controlled by formulas of Vapnik-Chervonenkis codimension 1
Hans H. Adler · 2008
The notion of a VC-minimal theory is introduced, a slightly more general variant of Cminimality that also includes all strongly minimal or (weakly) o-minimal theories. The 1dimensional definable sets in a VC-minimal theory have a good ‘swiss cheese’ representation similar to the C-minimal case. VC-minimal theories are dp-minimal; in particular they do not have the independence property, and if they are stable then every 1-type has weight 1.