We show that cov(M) is the least infinite cardinal λ such that $P_ω(λ)$ (the set of all finite subsets of λ ) fails to satisfy a certain natural generalization of Ramsey's Theorem.
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The paper is concerned with the computation of covering numbers in the presence of large cardinals. In particular, we revisit Solovay's result that the Singular Cardinal Hypothesis holds above a strongly compact cardinal.
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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.
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