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    • CommentRowNumber1.
    • CommentAuthorDavidRoberts
    • CommentTimeApr 26th 2012

    Mike added two new relevant links to WISC.

    I added a section about internal WISC, and changed what was about ’internal WISC’ to ’external WISC in other categories’.

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeJan 2nd 2013

    Asaf Karagila (some may know from MO or m.SE) has a new preprint which shows the independence of WISC from ZF without large cardinals, as Benno van den Berg does. I’ve added the reference to the page WISC.

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJan 3rd 2013

    Very interesting!

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeJan 4th 2013
    Yes, it's along the lines I think I can also prove it, but he is more familiar with forcing and ZF set theory. He actually proves something stronger in that one can ask for dependent choice to hold up to a fixed cardinal at the same time. All this means is that the WISC violating set is this cardinal, rather than say ω.

    I have ideas about a structural proof, but it requires translating certain lemmas about class forcing to results about toposes.
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