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Fragments of strong compactness, families of partitions and ideal extensions

Volume 234 / 2016

Laura Fontanella, Pierre Matet Fundamenta Mathematicae 234 (2016), 171-190 MSC: Primary 03E55, 03E02; Secondary 03E05. DOI: 10.4064/fm172-1-2016 Published online: 9 March 2016


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 $\mathcal {P}_\kappa (\lambda )$ of the canonical Ramsey theorem for pairs.


  • Laura FontanellaEinstein Institute of Mathematics
    Hebrew University of Jerusalem
    Edmund Safra Campus
    Givat Ram, Jerusalem, Israel
  • Pierre MatetLaboratoire de Mathématiques Nicolas Oresme
    Université de Caen – CNRS
    BP 5186
    14032 Caen Cedex, France

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