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

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Friedman S.-D., Halilović A.

Fundamenta Mathematicae

2013

tom 223

nr 1

55-64

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 $.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Friedman S.-D.

1 Halilović A.

1 2013

Wyniki wyszukiwania

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