The Diversity of Minimal Cofinal Extensions

2021/09/16 by Schmerl, James H.
#03C62 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2109.08130

Abstract

Fix a countable nonstandard model \mathcal M of Peano Arithmetic. Even with some rather severe restrictions placed on the types of minimal cofinal extensions \mathcal N \succ \mathcal M that are allowed, we still find that there are 2^ℵ₀ possible theories of (\mathcal N,M) for such \mathcal N's.

Related

• Lofty Models of Peano Arithmetic
• Cofinal Extensions and Coded Sets
• Model-theoretic applications of cofinality spectrum problems
• Models of expansions of N with no end extensions
• The Pentagon as a Substructure Lattice of Models of Peano Arithmetic