It is well-known that the family of automorphisms of any structure constitutes a topological group. In the late 1980s and 1990s, significant progress was made in the understanding of the automorphism group of models of Peano arithmetic (PA). In particular, Richard Kaye provided a landmark characterization of the closed normal subgroups of the automorphism group of a countable recursively saturated model M of PA. His work established an infinite Galois-like correspondence between these closed normal subgroups and invariant initial segments of M. He also conjectured the existence of another correspondence between the non-closed normal subgroups of the automorphism group of M and its invariant initial segments; a conjecture which has remained unproved. In this talk, I will first revisit Kaye�s characterization, and then explore some progress on his conjecture, confirming it in some cases.

Zoom room information:
https://us06web.zoom.us/j/81916335336?pwd=5zQT4lutMiBoY5Xp1pkFGtbqiaGozg.1
Meeting ID: 819 1633 5336
Passcode: 559618