Sh:893

• Shelah, S. (2015). A.E.C. with not too many models. In A. Hirvonen, M. Kesala, J. Kontinen, R. Kossak, & A. Villaveces, eds., Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics, Vols. Ontos Mathematical Logic, vol. 5, Berlin, Boston: DeGruyter, pp. 367–402. arXiv: 1302.4841 DOI: 10.1515/9781614516873.367
• Abstract:
  Consider an a.e.c. {\mathfrak K} and the class of {\mathbf C}_{\aleph_0} cardinals of cofinality \aleph_0. A nicely stated consequence of this work is for some closed unbounded class C of cardinals we have

  (a)\dot I(\lambda,{\mathfrak K})\geq \lambda for \lambda \in C \cap {\mathbf C_{\aleph_0}}

  or

  (b)if M \in K_\lambda and \lambda \in {\mathbf C}_{\aleph_0}, then M has \le_{\mathfrak K}-extension (so in {\mathfrak K}) of arbitrarily large cardinals.

• Version 2024-05-09 (35p) published version (36p)

@incollection{Sh:893,
 author = {Shelah, Saharon},
 title = {{A.E.C. with not too many models}},
 booktitle = {{Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics}},
 volume = {Ontos Mathematical Logic, vol. 5},
 year = {2015},
 pages = {367--402},
 publisher = {Berlin, Boston: DeGruyter},
 editor = {A. Hirvonen and M. Kesala and J. Kontinen and R. Kossak and A. Villaveces},
 doi = {10.1515/9781614516873.367},
 note = {\href{https://arxiv.org/abs/1302.4841}{arXiv: 1302.4841}},
 arxiv_number = {1302.4841}
}