Logic Seminar

Wednesday, March 17, 2021 2:00 pm - 2:00 pm EDT (GMT -04:00)

Marco Handa, Department of Pure Mathematics, University of Waterloo

"Internality in stable theories"

Internality is a central concept in geometric stability theory, which drives many applications of model theory to other mathematical disciplines. On the level of definable sets, internality expresses a relationship between two sets that is akin to one living in some Cartesian power of the other, except we replace "living in" with "being definably isomorphic to a subset of." A crucial part of the definition is that we allow the isomorphism to be defined over additional parameters, beyond those required to define the sets in question. When one considers a definable set that is internal to another, it is natural to ask how many additional parameters are needed to witness internality. This question is answered to some extent by an object called the binding group. This talk will introduce the model theoretic terminology necessary to define internality, then give an example of a set that is internal to the set of constants in a differential field, along with a computation of its binding group. If time permits, it will also include a discussion of some strengthenings of internality that have been introduced in the literature over the past few years. This will be an expository talk.

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