# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## Measurable cardinals and the cofinality of the symmetric group

### Tom 207 / 2010

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.

Odśwież obrazek