Upcoming Events

Logic Colloquium

March 20, 2026, 4:10 PM

60 Evans Hall

Toby Meadows
UC Irvine

Found in translation: at the limit of the Hudetz program

This paper considers the question: what does it mean for two mathematical structures (or collections thereof) to be inter-definable? This question is particularly pertinent in philosophy of physics where theories are not generally amenable to first order axiomatization. The paper begins by explaining the difficulty of the problem and giving an overview of some naive responses that don’t work well. The middle section then gives an overview of the proposed framework. The underlying idea is to use set theory with atoms (or urelemente) to provide a structural approach to set theory in a ZFC-like setting. This results in a massive generalization of the theory of relative interpretation. The final section considers applications of the approach and closes with some problems for future work.

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.