Models of expansions of N with no end extensions

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of N such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of N such that expanding N by any uncountably many of them suffice. Also we find arithmetically closed A with no ultrafilter on it with suitable definability demand (related to being Ramsey).

Original languageEnglish
Pages (from-to)341-365
Number of pages25
JournalMathematical Logic Quarterly
Volume57
Issue number4
DOIs
StatePublished - Aug 2011

Keywords

  • End extensions
  • Forcing with creatures
  • Models of Peano arithmetic

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