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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| 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. |
| format | Article |
| id | doaj-art-231365f80a8a4725a2c8394df541e9c7 |
| institution | OA Journals |
| issn | 0567-8293 2464-7055 |
| language | ces |
| publishDate | 2025-02-01 |
| publisher | Karolinum Press |
| record_format | Article |
| 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 |
| work_keys_str_mv | AT radekhonzik therabinkeislertheoremandthesizesofultrapowers AT radekhonzik rabinkeislertheoremandthesizesofultrapowers |