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    • CommentRowNumber1.
    • CommentAuthorzskoda
    • CommentTimeMar 27th 2013
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeMar 27th 2013
    • (edited Mar 27th 2013)

    Thanks.

    I have added a link to this from modal logic.

    • CommentRowNumber3.
    • CommentAuthorTodd_Trimble
    • CommentTimeMar 27th 2013

    I’m not really understanding the theorem, but it sounds similar to the Birkhoff characterization of equational varieties.

    • CommentRowNumber4.
    • CommentAuthorTim_Porter
    • CommentTimeMar 29th 2013
    • (edited Mar 29th 2013)

    I am away from base so cannot check, but I seem to remember that it is exactly a relational version of Birkhoff’s theorem. There is a survey of Algebraic Polymodal Logic by Goldblatt that I have used and I remember that it has a discussion of the theorem. Note there is a paper linking the theorem with coalgebras. It starts:

    ”The Goldblatt-Thomason theorem [11] states that a class of Kripke frames closed under ultrafilter extensions is modally definable if and only if it reflects ultrafilter extensions and is closed under generated subframes, homomorphic images and disjoint unions….”

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