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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| Format: | Article |
| Language: | ces |
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Karolinum Press
2025-02-01
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| Series: | Acta Universitatis Carolinae: Philosophica et Historica |
| Online Access: | http://www.karolinum.cz/doi/10.14712/24647055.2025.3 |
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| Summary: | 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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| ISSN: | 0567-8293 2464-7055 |