Cofinal Extensions and Coded Sets

2017/08/02 by Schmerl, James H.
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1708.00899

Abstract

Let M be a model of Peano Arithmetic that is countably generated over an exponentially closed cut I. We characterize those sets X of subsets of I for which there is a finitely (or countably) generated cofinal extension N of M such that I is the Greatest Common Initial Segment of M and N and X is the set of subsets of I coded by the extension. We also characterize such X for which the extension N can be, in addition, one of the following: non-filling; filling; n-filling.

Related

• The Diversity of Minimal Cofinal Extensions
• Models of expansions of N with no end extensions
• The Pentagon as a Substructure Lattice of Models of Peano Arithmetic
• Model-theoretic applications of cofinality spectrum problems
• Minimal elementary end extensions