The Automorphism Group of a Resplendent Model

The first-order theory of the automorphism group of an infinite resplendent model in a finite language is undecidable

Automorphism Groups of Countable Arithmetically Saturated Models of Peano Arithmetic

If M,N are countable, arithmetically saturated models of Peano Arithmetic and Aut(M) is isomorphic to Aut(N), then the Turing-jumps of Th(M) and Th(N) are recursively equivalent.Comment: This version is a complete revision of the previous version. The main result of this version greatly improves the main result of the earlier versio