MidWest Model Theory Day

Tuesday, April 4, 2017 at UIC

Spring 2017 MWMT is April 4.

: Erik Walsberg, Vince Guingona, Nadja Hempel

Schedule: All talks are about an hour long including questions, in SEO 636. There will also be coffee & cookies in 636.
It is probably easiest to park in the university parking lot on Morgan St. between Roosevelt and Taylor; please bring in parking tickets, and we can validate them.

Let us know (jfreitag at uic dot edu) if you are planning to come to lunch and/or dinner so we can make approximately correct reservations!

Speaker: Vince Guingona
Title: Fraisse classes and model-theoretic dividing lines
Abstract: I discuss the notion of positive local combinatorial dividing lines in model theory, showing how these relate to certain Fraisse classes.  I examine this relationship vis-a-vis several well-known examples, including stability, NIP, and n-dependence.  I also explore the question of when two Fraisse classes give rise to the same dividing line.
This work is joint with C. D. Hill.

Speaker: Nadja Hempel
Title: Mekler constructions in NIP and n-dependent theories
Abstract: Given a so called nice graph (no triangles, no squares, for any choice of two distinct vertices there is a third vertex which is connected to one and not the other), Mekler considered the 2-nilpotent subgroup generated by the vertices of the graph in which two elements given by vertices commute if and only if there is an edge between them. These groups form an interesting collection of examples from a model theoretic point of view. It was shown that such a group is stable if and only if the corresponding graph is stable and Baudisch generalized this fact to the simple theory context. In a joint work with Chernikov, we were able to verify this result for NIP and even n-dependent theories. This leads to the existence of groups which are (n+1)-dependent but not n-dependent, providing the first algebraic objects witnessing the strictness of these hierarchy (work in progress).