Submission date: 24 April 2022

Abstract:

In this paper we will show that for every cut I of any countable nonstandard model M of IΣ_{1} , each I -small Σ_{1} -elementary submodel of M is of the form of the set of fixed points of some proper initial self-embedding of M iff I is a strong cut of M. Especially, this feature will provide us with some equivalent conditions with the strongness of the standard cut in a given countable model M of IΣ_{1} . In addition, we will find some criteria for extendability of initial self-embeddings of countable nonstandard models of IΣ_{1} to larger models.

Mathematics Subject Classification:

Keywords and phrases:

Full text arXiv 2204.11284: pdf, ps.