# 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 2015-05-08_12 (34p) published version (36p)

Bib entry

@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} }