Upcoming Events

Logic Colloquium

February 13, 2026, 4:10 PM

60 Evans Hall

Dominik Adolf
Harbin Institute of Technology

The great determinacy translation project

A large part of modern set theory is about proving the relative consistency of two theories (incompleteness, of course, is the reason we do not try for a proof of absolute consistency). For efficiency, one should measure the relative consistency strength of a given theory (an extension of ZFC, usually) against a fixed hierarchy of natural theories. Traditionally, the hierarchy of Large Cardinal Axioms, generalizations of the Axiom of Infinity, have served this purpose. In the development of Inner Model Theory, one of the two pillars of relative consistency proofs, a second hierarchy has increasingly moved into a position of extreme importance. A hierarchy of axioms positing the determinacy of certain two player games with perfect information played on natural numbers.

In this talk, we want to discuss parts of our current research project that aims to find a natural correspondence between these two hierarchies by linking the structure of canonical models of ZFC (so called mice) with the structure of associated (via Woodin’s derived model theorem) models of determinacy. We hope that this project will lead towards a comprehensive procedure to ‘translate’ between theories of large cardinals and determinacy. This is joint work with Sandra Müller and Benjamin Siskind.

Logic Colloquium

March 06, 2026, 4:10 PM

60 Evans Hall

Anton Bernshteyn
UCLA

Logic Colloquium

March 13, 2026, 4:10 PM

60 Evans Hall

Anand Pillay
University of Notre Dame

Logic Colloquium

March 20, 2026, 4:10 PM

60 Evans Hall

Toby Meadows
UC Irvine

Logic Colloquium

April 17, 2026, 4:10 PM

60 Evans Hall

Thomas Barrett
UC Santa Barbara