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Thursday, October 19, 2017

4:20 PM - 5:20 PM (ET)

Exley Science Center Tower ESC 121

Event Type

Seminar/Colloquium

Contact

Canalia, Caryn

2182

Link

https://eaglet.wesleyan.edu/MasterCalendar/EventDetails.aspx?EventDetailId=79077

Speaker: Alex Kruckman, Indiana University-Bloomington

Title: First-order logic and cologic over a category

** Abstract:
**In ordinary first-order logic, each formula comes with a finite
variable context. In order to assign a truth value to the formula, we need an
interpretation of its context: an assignment of the variables to elements of a
structure. I will describe a categorical generalization of first-order logic,
obtained by replacing the category of finite sets (variable contexts) with any small
category C with finite colimits, and replacing arbitrary sets (domains of
structures) with formal directed colimits from C. I will present a deductive
system and completeness theorem for this logic, which is related to
hyperdoctrines, a notion from categorical logic. Once this categorical
framework is in place, it is easily dualizable. The result is a first-order
"cologic", which is well-suited for studying profinite structures in
terms of their finite quotients; indeed, this was the original motivation. As
particular examples, I will explain how the framework includes the
"cologic" of profinite groups due to Cherlin, Macintyre, and van den
Dries, and the theories of projective Fraisse limits due to Solecki and Irwin.