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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.