Title: Separation for isometric group actions, and algebraic closure in continuous logic
Speaker: Gabriel Conant (The Ohio State University)
Speaker's URL: https://people.math.osu.edu/conant.38/
Abstract: This talk will be about a certain strong amalgamation property satisfied by algebraic closure in first-order structures. In particular, given a complete type p over some parameter set C, and some other parameter set B, one can always find a realization of p whose only algebraic interaction with B comes from parameters in C. This folklore fact is a key tool in certain proofs of elimination of imaginaries, and also in properties of forking and dividing. Around 2012, Goldbring asked if the same result can be proved for algebraic closure in "continuous model theory" (i.e., the model theory of metric structures). I will show how a positive answer can be obtained by adapting classical results on permutation groups to the setting of group actions on metric spaces. This is joint work with James Hanson (Maryland).