AUC Philosophica et Historica (Acta Universitatis Carolinae Philosophica et Historica) is a multidisciplinary academic journal focused on the humanities with more than 50 years of tradition.
The journal is indexed in CEEOL, DOAJ, and EBSCO.
AUC PHILOSOPHICA ET HISTORICA, Vol 2022 No 1 (2022), 45–55
The Rabin-Keisler theorem and the sizes of ultrapowers
Radek Honzík
DOI: https://doi.org/10.14712/24647055.2025.3
published online: 28. 02. 2025
abstract
Recall the Rabin-Keisler theorem which gives a lower bound κω for the size of proper elementary extensions of complete structures of size κ, provided that κ is an infinite cardinal below the first measurable cardinal. We survey – and at places clarify and extend – some facts which connect the Rabin-Keisler theorem, sizes of ultrapowers, combinatorial properties of ultrafilters, and large cardinals.
keywords: Rabin-Keisler theorem; sizes of ultrapowers; non-regular ultrafilters
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The Rabin-Keisler theorem and the sizes of ultrapowers is licensed under a Creative Commons Attribution 4.0 International License.
