Submission date: 12 May 2022

Abstract:

This is a survey of results on definability and undefinability in models of arithmetic. The goal is to present a stark difference between undefinability results in the standard model and much stronger versions about expansions of nonstandard models. The key role is played by counting the number of automorphic images of subsets of countable resplendent models of Peano Arithmetic.

Mathematics Subject Classification: 03C62, 03H15

Keywords and phrases:

Full text arXiv 2205.06022: pdf, ps.