The Rabin-Keisler theorem and the sizes of ultrapowers
The Rabin-Keisler theorem and the sizes of ultrapowers
Author(s): Radek HonzíkSubject(s): Philosophy, Metaphysics, Epistemology, Logic, Philosophy of Science
Published by: Univerzita Karlova v Praze, Nakladatelství Karolinum
Keywords: Rabin-Keisler theorem; sizes of ultrapowers; non-regular ultrafilters
Summary/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.
Journal: Acta Universitatis Carolinae Philosophica et Historica
- Issue Year: XXVIII/2022
- Issue No: 1
- Page Range: 45-55
- Page Count: 11
- Language: English
