AUTOMORPHISM GROUPS OF COUNTABLE ARITHMETICALLY SATURATED MODELS OF PEANO ARITHMETIC

Abstract

AbstractIf ${\cal M},{\cal N}$ are countable, arithmetically saturated models of Peano Arithmetic and ${\rm{Aut}}\left( {\cal M} \right) \cong {\rm{Aut}}\left( {\cal N} \right)$, then the Turing-jumps of ${\rm{Th}}\left( {\cal M} \right)$ and ${\rm{Th}}\left( {\cal N} \right)$ are recursively equivalent.