# Sh:937

• Shelah, S. (2011). Models of expansions of \mathbb N with no end extensions. MLQ Math. Log. Q., 57(4), 341–365.
• 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 \mathbb N such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of \mathbb N such that expanding \mathbb N by any uncountably many of them suffice. Also we find arithmetically closed {\mathcal A} with no definably closed ultrafilter on it
• Current version: 2010-06-06_10 (26p) published version (25p)
Bib entry
@article{Sh:937,
author = {Shelah, Saharon},
title = {{Models of expansions of $\mathbb N$ with no end extensions}},
journal = {MLQ Math. Log. Q.},
fjournal = {MLQ. Mathematical Logic Quarterly},
volume = {57},
number = {4},
year = {2011},
pages = {341--365},
issn = {0942-5616},
mrnumber = {2832642},
mrclass = {03C62 (03E35 03E40)},
doi = {10.1002/malq.200910129},
note = {\href{https://arxiv.org/abs/0808.2960}{arXiv: 0808.2960}},
arxiv_number = {0808.2960}
}