# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## The tree property at the double successor of a measurable cardinal $\kappa$ with $2^{\kappa}$ large

### Tom 223 / 2013

Fundamenta Mathematicae 223 (2013), 55-64 MSC: 03E35, 03E55. DOI: 10.4064/fm223-1-4

#### Streszczenie

Assuming the existence of a $\lambda ^+$-hypermeasurable cardinal $\kappa$, where $\lambda$ is the first weakly compact cardinal above $\kappa$, we prove that, in some forcing extension, $\kappa$ is still measurable, $\kappa ^{++}$ has the tree property and $2^\kappa =\kappa ^{+++}$. If the assumption is strengthened to the existence of a $\theta$-hypermeasurable cardinal (for an arbitrary cardinal $\theta >\lambda$ of cofinality greater than $\kappa$) then the proof can be generalized to get $2^\kappa =\theta$.

#### Autorzy

• Sy-David FriedmanKurt Gödel Research Center
University of Vienna
1090 Wien, Austria
e-mail
• Ajdin HalilovićFaculty of Engineering Sciences
Lumina–The University of South East Europe
021187 Bucureşti, Romania
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek