On 21 May 2011, at 19:15, meekerdb wrote:

On 5/21/2011 4:43 AM, Bruno Marchal wrote:
3-OMs are sequenced by the computations they "belongs" too. 1-OM are structured by the topology on those computations derived from the application of Theaetetus' theory of knowledge.

What topology is that?  What's the open set?

The topology you can associate to the open set semantics, or neighborhood semantics of the intuitionistic logic corresponding to the inverse of Goldblatt-Boolos-Grzegorczyk from S4Grz logic representation in G, when the arithmetical interpretation is restricted to the sigma_1 prposition, that is the logic I call S4Grz1. And the same for X1*, except that the transformation is different, and use another reporesentation theorem by Goldblatt. Some more recent works by Ysapia and Blok suggest Scattered Hausdorff topological spaces.
But it is highly technical and beyond the scope of the list, I think.



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