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    • CommentRowNumber1.
    • CommentAuthorfastlane69
    • CommentTimeMay 31st 2016

    Came across this today:

    the new proof settles a question that has eluded top experts for two decades: the classification of a statement known as “Ramsey’s theorem for pairs,”

    I couldn’t help but think of topos and subobject quantifiers when I heard this. Are they related? Does CT or nPOV have anything to say about this? Any thoughts on this subject?

    • CommentRowNumber2.
    • CommentAuthorUlrik
    • CommentTimeJun 1st 2016

    I don’t think the two kinds of “classification” are particularly related. The kind of classification here (i.e., determining the possible sets of Π 2 0\Pi^0_2 or Π 3 0\Pi^0_3 consequences of RT 2 nRT^n_2 as nn varies) is more akin to the classification of surfaces or finite simple groups: give a concrete description of the possibilities as a variable ranges over a domain. In contrast, a classifying space gives a correspondence between a kind of structure on any space and maps into the classifying space.