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2021-05-06

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cc by (c) Lücke, Philipp et al., 2021
Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/229964

Closure properties of measurable ultrapowers

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Recurs relacionat

https://doi.org/10.1017/jsl.2021.29

Resum

We study closure properties of measurable ultrapowers with respect to Hamkin’s notion of freshness and show that the extent of these properties highly depends on the combinatorial properties of the underlying model of set theory. In one direction, a result of Sakai shows that, by collapsing a strongly compact cardinal to become the double successor of a measurable cardinal, it is possible to obtain a model of set theory in which such ultrapowers possess the strongest possible closure properties. In the other direction, we use various square principles to show that measurable ultrapowers of canonical inner models only possess the minimal amount of closure properties. In addition, the techniques developed in the proofs of these results also allow us to derive statements about the consistency strength of the existence of measurable ultrapowers with non-minimal closure properties.

Matèries

Teoria de conjunts, Teoria combinatòria de conjunts, Lògica

Matèries (anglès)

Set theory, Combinatorial set theory, Logic

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Articles publicats en revistes (Matemàtiques i Informàtica)

Citació

LÜCKE, Philipp and MÜLLER, Sandra. Closure properties of measurable ultrapowers. Journal of Symbolic Logic. 2021. Vol. 86, num. 2, pags. 762-784. ISSN 0022-4812. [consulted: 27 of June of 2026]. Available at: https://hdl.handle.net/2445/229964

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