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1. • CommentRowNumber1.
   • CommentAuthorzskoda
   • CommentTimeMar 27th 2013
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   Author: zskoda
   Format: MarkdownItex[[Goldblatt-Thomason theorem]]

   Goldblatt-Thomason theorem

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMar 27th 2013
   • (edited Mar 27th 2013)
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   Author: Urs
   Format: MarkdownItexThanks. I have added a link to this from _[[modal logic]]_.

   Thanks.

   I have added a link to this from modal logic.

3. • CommentRowNumber3.
   • CommentAuthorTodd_Trimble
   • CommentTimeMar 27th 2013
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   Author: Todd_Trimble
   Format: MarkdownItexI'm not really understanding the theorem, but it sounds similar to the [Birkhoff characterization](http://en.wikipedia.org/wiki/Variety_%28universal_algebra%29#Birkhoff.27s_theorem) of equational varieties.

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

4. • CommentRowNumber4.
   • CommentAuthorTim_Porter
   • CommentTimeMar 29th 2013
   • (edited Mar 29th 2013)
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   Author: Tim_Porter
   Format: MarkdownItexI 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](http://homepages.mcs.vuw.ac.nz/~rob/papers/algpolylogic.pdf) 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](http://www.cs.le.ac.uk/people/akurz/Papers/CALCO-07/GTthm.pdf) 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....''

   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….”