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1. • CommentRowNumber1.
   • CommentAuthorfastlane69
   • CommentTimeMay 31st 2016
   • PermaLink
   Author: fastlane69
   Format: MarkdownItexCame 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,” ](http://www.wired.com/2016/05/mathematicians-bridge-divide-infinity-physical-world/#slide-2) 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?

   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?

2. • CommentRowNumber2.
   • CommentAuthorUlrik
   • CommentTimeJun 1st 2016
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   Author: Ulrik
   Format: MarkdownItexI don't think the two kinds of “classification” are particularly related. The kind of classification here (i.e., determining the possible sets of $\Pi^0_2$ or $\Pi^0_3$ consequences of $RT^n_2$ as $n$ 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.

   I don’t think the two kinds of “classification” are particularly related. The kind of classification here (i.e., determining the possible sets of $\Pi^0_2$ or $\Pi^0_3$ consequences of $RT^n_2$ as $n$ 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.