# Sh:1092

- Baldwin, J. T., & Shelah, S. (2022).
*Hanf numbers for extendibility and related phenomena*. Arch. Math. Logic,**61**(3-4), 437â€“464. arXiv: 2111.01704 DOI: 10.1007/s00153-021-00796-1 MR: 4418753 -
Abstract:

In this paper we discuss two theorems whose proofs depend on extensions of the FraissÃ© 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} }