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The tree property at both $ℵ_{ω+1}$ and $ℵ_{ω+2}$

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Fontanella L., Friedman S.

Fundamenta Mathematicae

2015

tom 229

nr 1

83-100

We force from large cardinals a model of ZFC in which $ℵ_{ω+1}$ and $ℵ_{ω+2}$ both have the tree property. We also prove that if we strengthen the large cardinal assumptions, then in the final model $ℵ_{ω+2}$ even satisfies the super tree property.

Fragments of strong compactness, families of partitions and ideal extensions

100%

Fontanella L., Matet P.

Fundamenta Mathematicae

2016

tom 234

nr 2

171-190

We investigate some natural combinatorial principles related to the notion of mild ineffability, and use them to obtain new characterizations of mild ineffable and weakly compact cardinals. We also show that one of these principles may be satisfied by a successor cardinal. Finally, we establish a version for $𝓟_{κ}(λ)$ of the canonical Ramsey theorem for pairs.

Ograniczanie wyników

2 Fundamenta Mathematicae

2 Fontanella L.

1 Friedman S.

1 Matet P.

1 2016

1 2015

Wyniki wyszukiwania

The tree property at both $ℵ_{ω+1}$ and $ℵ_{ω+2}$

Fragments of strong compactness, families of partitions and ideal extensions