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 language | English |
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Pages (from-to) | 341-365 |
Number of pages | 25 |
Journal | Mathematical Logic Quarterly |
Volume | 57 |
Issue number | 4 |
DOIs | |
State | Published - Aug 2011 |
Keywords
- End extensions
- Forcing with creatures
- Models of Peano arithmetic