Measurable cardinals and the cofinality of the symmetric group

Tom 207 / 2010

Sy-David Friedman, Lyubomyr Zdomskyy Fundamenta Mathematicae 207 (2010), 101-122 MSC: Primary 03E35; Secondary 03E55, 03E99. DOI: 10.4064/fm207-2-1

Streszczenie

Assuming the existence of a $P_2\kappa$-hypermeasurable cardinal, we construct a model of Set Theory with a measurable cardinal $\kappa$ such that $2^\kappa=\kappa^{++}$ and the group ${\it Sym}(\kappa)$ of all permutations of $\kappa$ cannot be written as the union of a chain of proper subgroups of length $<\kappa^{++}$. 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)].

Autorzy

  • Sy-David FriedmanKurt Gödel Research Center for Mathematical Logic
    University of Vienna
    Währinger Strasse 25
    A-1090 Wien, Austria
    e-mail
  • Lyubomyr ZdomskyyKurt Gödel Research Center for Mathematical Logic
    University of Vienna
    Währinger Strasse 25
    A-1090 Wien, Austria
    e-mail

Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Przepisz kod z obrazka

Odśwież obrazek

Odśwież obrazek