The Rabin-Keisler theorem and the sizes of ultrapowers

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-...

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Main Author: Radek Honzík
Format: Article
Language:ces
Published: Karolinum Press 2025-02-01
Series:Acta Universitatis Carolinae: Philosophica et Historica
Online Access:http://www.karolinum.cz/doi/10.14712/24647055.2025.3
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author Radek Honzík
author_facet Radek Honzík
author_sort Radek Honzík
collection DOAJ
description 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.
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2464-7055
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publisher Karolinum Press
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series Acta Universitatis Carolinae: Philosophica et Historica
spelling doaj-art-231365f80a8a4725a2c8394df541e9c72025-08-20T02:11:08ZcesKarolinum PressActa Universitatis Carolinae: Philosophica et Historica0567-82932464-70552025-02-0120221455510.14712/24647055.2025.3The Rabin-Keisler theorem and the sizes of ultrapowersRadek HonzíkRecall 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.http://www.karolinum.cz/doi/10.14712/24647055.2025.3
spellingShingle Radek Honzík
The Rabin-Keisler theorem and the sizes of ultrapowers
Acta Universitatis Carolinae: Philosophica et Historica
title The Rabin-Keisler theorem and the sizes of ultrapowers
title_full The Rabin-Keisler theorem and the sizes of ultrapowers
title_fullStr The Rabin-Keisler theorem and the sizes of ultrapowers
title_full_unstemmed The Rabin-Keisler theorem and the sizes of ultrapowers
title_short The Rabin-Keisler theorem and the sizes of ultrapowers
title_sort rabin keisler theorem and the sizes of ultrapowers
url http://www.karolinum.cz/doi/10.14712/24647055.2025.3
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