Expansions of geometric theories as measurable structures

Abstract: We say that a theory T is geometric if for any model $M\models T$ the algebraic closure satisfies the exchange property and T eliminates the quantifier $\exists^{\infty}$. We will explain how to define, inside a geometric theory, a well behaved notion of dimension for definable sets. We will then consider the special case where the underlying theory is measurable (in the sense of Macpherson and Steinhorn) of SU-rk one, where besides a dimension we can also assign a measure to definable sets. We will then introduce an expansion called an H-structures and show that it can be studied as a generalized measurable structure whose dimension has values in $\omega^2$. This is joint work with García and Zou.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic