Sh:1092
- Baldwin, J. T., & Shelah, S. (2022). Hanf numbers for extendibility and related phenomena. Arch. Math. Logic, 61(3-4), 437–464. arXiv: 2111.01704 DOI: 10.1007/s00153-021-00796-1 MR: 4418753
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Abstract:
In this paper we discuss two theorems whose proofs depend on extensions of the Fraissé method. We prove the Hanf number for the existence of an extendible model (has a proper extension in the class. Here, this means an \infty,\omega-elementary extension) of a (complete) sentence of L_{\omega_1, \omega} is (modulo some mild set theoretic hypotheses that we expect to remove in a later paper) the first measurable cardinal. And we outline the description on an explicit L_{\omega_1, \omega}-sentence \phi_n characterizing \aleph_n for each n. We provide some context for these developments as outlined in the lectures at IPM. - Version 2021-01-09 (26p) published version (28p)
Bib entry
@article{Sh:1092,
author = {Baldwin, John T. and Shelah, Saharon},
title = {{Hanf numbers for extendibility and related phenomena}},
journal = {Arch. Math. Logic},
fjournal = {Archive for Mathematical Logic},
volume = {61},
number = {3-4},
year = {2022},
pages = {437--464},
issn = {0933-5846},
mrnumber = {4418753},
mrclass = {03C55 (03E55)},
doi = {10.1007/s00153-021-00796-1},
note = {\href{https://arxiv.org/abs/2111.01704}{arXiv: 2111.01704}},
arxiv_number = {2111.01704}
}