Hanf numbers for extendibility and related phenomena

Hanf numbers for extendibility and related phenomena This paper contains portions of Baldwin’s talk at the Set Theory and Model Theory Conference (Institute for Research in Fundamental Sciences, Tehran, October 2015) and a detailed proof that in a suitable extension of ZFC, there is a complete sentence of Lω1,ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L_{\omega _1,\omega }$$\end{document} that has maximal models in cardinals cofinal in the first measurable cardinal and, of course, never again. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Archive for Mathematical Logic Springer Journals

Hanf numbers for extendibility and related phenomena

, Volume OnlineFirst – Oct 13, 2021
28 pages

/lp/springer-journals/hanf-numbers-for-extendibility-and-related-phenomena-xA9JaleluW
Publisher
Springer Journals
Copyright © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021
ISSN
0933-5846
eISSN
1432-0665
DOI
10.1007/s00153-021-00796-1
Publisher site
See Article on Publisher Site

Abstract

This paper contains portions of Baldwin’s talk at the Set Theory and Model Theory Conference (Institute for Research in Fundamental Sciences, Tehran, October 2015) and a detailed proof that in a suitable extension of ZFC, there is a complete sentence of Lω1,ω\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$L_{\omega _1,\omega }$$\end{document} that has maximal models in cardinals cofinal in the first measurable cardinal and, of course, never again.

Journal

Archive for Mathematical LogicSpringer Journals

Published: Oct 13, 2021

Keywords: Hanf numbers; Maximal models; Lω1ω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{\omega _1 \omega }$$\end{document}; Measurable cardinals; Amalgamation