Some ideas at the border of infinite combinatorics, model theory, and category theory

This is the title of a talk to be given at the Snapshot of math at Harvard conference on April 14, 2018.

Abstract

Imagine blending together category theory, infinite combinatorics, and model theory. What field of mathematics will you get, and what will it taste like? I will attempt to answer this in less than twenty minutes. No prerequisites needed!

References

• John T. Baldwin, Categoricity, University Lecture Series, vol. 50, American Mathematical Society, 2009.

• Saharon Shelah, Classification Theory for Abstract Elementary Classes, Studies in Logic: Mathematical Logic and foundations, vols. 18 and 20, College Publications, 2009.

• Sebastien Vasey, Shelah's eventual categoricity conjecture in universal classes. Part I, Annals of Pure and Applied Logic 168 (2017), no. 9, 1609–1642. Publisher version pdf arXiv.

• Sebastien Vasey, Shelah's eventual categoricity conjecture in universal classes. Part II, Selecta Mathematica 23 (2017), no. 2, 1469–1506. Publisher version pdf arXiv.

• Sebastien Vasey, Tameness from two successive good frames, Submitted. Preprint: pdf arXiv, 25 pages.