# Sh:1092

- Baldwin, J. T., & Shelah, S.
*Hanf numbers for extendibility and related phenomena*. Preprint. -
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)

Bib entry

@article{Sh:1092, author = {Baldwin, John T. and Shelah, Saharon}, title = {{Hanf numbers for extendibility and related phenomena}} }