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

• Autorzy: Sy-David Friedman , Ajdin Halilović
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 03E55: Large cardinals
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2013
• Tom: 223
• Numer: 1
• Strony: 55-64

Daty

wydano

2013

Twórcy

autor

Sy-David Friedman

• Kurt Gödel Research Center, University of Vienna, 1090 Wien, Austria

autor

Ajdin Halilović

• Faculty of Engineering Sciences, Lumina-The University of South East Europe, 021187 Bucureşti, Romania

Identyfikatory

DOI

10.4064/fm223-1-4