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
• Version 2010-06-06_11 (26p) published version (25p)

@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}
}