A model of Peano Arithmetic is short recursively saturated if it realizes all its bounded finitely realized recursive types. Short recursively saturated models of are exactly the elementary initial segments of recursively saturated models of . In this paper, we survey and prove results on short recursively saturated models of and their automorphisms. In particular, we investigate a certain subgroup of the automorphism group of such models. This subgroup, denoted , contains all the automorphisms of a countable short recursively saturated model of which can be extended to an automorphism of the countable recursively saturated elementary end extension of the model.
"Automorphisms of Countable Short Recursively Saturated Models of PA." Notre Dame J. Formal Logic 49 (4) 345 - 360, 2008. https://doi.org/10.1215/00294527-2008-016