1,003 research outputs found

    A general tool for consistency results related to I1

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    In this paper we provide a general tool to prove the consistency of I1(λ)I1(\lambda) with various combinatorial properties at λ\lambda typical at settings with 2λ>λ+2^\lambda>\lambda^+, that does not need a profound knowledge of the forcing notions involved. Examples of such properties are the first failure of GCH, a very good scale and the negation of the approachability property, or the tree property at λ+\lambda^+ and λ++\lambda^{++}

    The singular world of singular cardinals

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    The article uses two examples to explore the statement that, contrary to the common wisdom, the properties of singular cardinals are actually more intuitive than those of the regular ones

    Club-guessing, stationary reflection, and coloring theorems

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    We obtain strong coloring theorems at successors of singular cardinals from failures of certain instances of simultaneous reflection of stationary sets. Along the way, we establish new results in club-guessing and in the general theory of ideals.Comment: Initial public versio
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