Fragments of strong compactness, families of partitions and ideal extensions

Laura Fontanella (1) , Pierre Matet (2)

1 Einstein Institute of Mathematics
2 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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 Pκ(λ) of the canonical Ramsey theorem for pairs.

Domaines: Logique [math.LO]

Laura Fontanella, Pierre Matet. Fragments of strong compactness, families of partitions and ideal extensions. Fundamenta Mathematicae, 2016, 234, pp.1-20. ⟨10.4064/fm172-1-2016⟩. ⟨hal-02145603⟩