The Rabin-Keisler theorem and the sizes of ultrapowers

Radek Honzík

The Rabin-Keisler theorem and the sizes of ultrapowers

Číslo: 1/2022
Periodikum: Acta Universitatis Carolinae Philosophica et Historica
DOI: 10.14712/24647055.2025.3

Klíčová slova: Rabin-Keisler theorem; sizes of ultrapowers; non-regular ultrafilters

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Anotace: 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.