[Alta-Logic] Reminder: Talk Today: Structural set theory

[gscruttw at ucalgary.ca]

Talk today by Mike Shulman, visiting this week from the University of
Chicago:

Structural set theory

Set theory is central to modern mathematics, but axiomatic set
theories such as ZF are somewhat mismatched to mathematical practice:
they include superfluous structure, draw irrelevant distinctions, and
permit nonsensical questions.  These problems are avoided by
"structural" set theories, such as Lawvere's "Elementary Theory of the
Category of Sets (ETCS)," in which distinct abstract sets never share
elements and cannot be compared for equality (only isomorphism).
Structural set theories are closely related to category theory and
type theory, and thus hold the promise of a fruitful bridge between
these fields and axiomatic set theory.

In this talk, I'll explain how structural set theory provides a
convenient and natural framework for mathematics.  Then I'll describe
some recent work which strengthens the connection between category
theory and set theory, by interpreting unbounded quantifiers
category-theoretically by means of structural set theory.  This allows
a more direct translation of set-theoretic notions into
category-theoretic language, and of category-theoretic constructions
into set-theoretic models.

Place and time: Wed March 24th, 2:30pm, in SS 1253.