# Sh:937

- Shelah, S. (2011).
*Models of expansions of \mathbb N with no end extensions*. MLQ Math. Log. Q.,**57**(4), 341–365. arXiv: 0808.2960 DOI: 10.1002/malq.200910129 MR: 2832642 -
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 - 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}, doi = {10.1002/malq.200910129}, mrclass = {03C62 (03E35 03E40)}, mrnumber = {2832642}, mrreviewer = {Roman Kossak}, doi = {10.1002/malq.200910129}, note = {\href{https://arxiv.org/abs/0808.2960}{arXiv: 0808.2960}}, arxiv_number = {0808.2960} }