Upcoming Events

Logic Colloquium

March 13, 2026, 4:10 PM

60 Evans Hall

Anand Pillay
University of Notre Dame

Remarks on relative categoricity

Relative categoricity (also called categoricity over a predicate) was introduced by Haim Gaifman in the paper “Operations on relational structures, functors, classes” appearing in the 1974 proceedings of the 1971 Tarski symposium. The first part of my 1977 thesis was around trying to solve the “Gaifman conjecture” which, amazingly, is still open in its full entirety. I will discuss work over the years around relative categoricity, relative stability, and the “Gaifman conjecture”, including a new modest contribution (which could and should have appeared in my thesis).

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

Invariance and Definability in General Relativity

Definability is well understood in the context of model theory. In this talk we will investigate several precise notions of definability for relativistic spacetimes. We show that there is a hierarchy of notions of implicit definability paralleling the ‘asymmetry hierarchy’ of Manchak and Barrett (2024), and we compare these notions with a few others. In general these varieties of definability stand in strict implication relations, though important special cases arise in which parts of the hierarchy collapse. We conclude by using these results to clarify the relationship between symmetry, definability, and structure in general relativity.