Fixed Sets of Automorphisms of Countable, Arithmetically Saturated Structures

TL;DR

This paper characterizes the possible substructure types fixed by automorphisms with a specific fixed-point property in countable, arithmetically saturated structures, advancing understanding of automorphism groups in model theory.

Contribution

It provides a complete characterization of the isomorphism types of fixed substructures under certain automorphisms in countable, arithmetically saturated structures.

Findings

Characterization of fixed substructure types for automorphisms with fixed-point properties

Identification of conditions under which fixed substructures are isomorphic to specific structures

Extension of automorphism theory in arithmetically saturated models

Abstract

If an automorphism f of a structure M is such that fix(f^k) = fix(f) for all positive k, then M|fix(f) is a substructure of M. The possible isomorphism types of such M|fix(f) are characterized when M is countable and arithmetically saturated.