Measurable cardinals and the cofinality of the symmetric group

• Autorzy: Sy-David Friedman , Lyubomyr Zdomskyy
• Języki publikacji: EN

Abstrakty

EN

Assuming the existence of a P₂κ-hypermeasurable cardinal, we construct a model of Set Theory with a measurable cardinal κ such that $2^{κ} = κ⁺⁺$ and the group Sym(κ) of all permutations of κ cannot be written as the union of a chain of proper subgroups of length < κ⁺⁺. The proof involves iteration of a suitably defined uncountable version of the Miller forcing poset as well as the "tuning fork" argument introduced by the first author and K. Thompson [J. Symbolic Logic 73 (2008)].

Kategorie tematyczne

• 03E55: Large cardinals
• 03E99: None of the above, but in this section
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 207
• Numer: 2
• Strony: 101-122

Daty

wydano

2010

Twórcy

autor

Sy-David Friedman

• Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, A-1090 Wien, Austria

autor

Lyubomyr Zdomskyy

• Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Währinger Strasse 25, A-1090 Wien, Austria

Identyfikatory

DOI

10.4064/fm207-2-1