[FOM] S5 models & RE sets
mcarroll at pobox.com
Fri Jun 4 00:26:05 EDT 2010
I've formulated a question I'm having trouble answering. I was hoping an
FOMer might help.
Take the modal propositional system S5 and Kripke models for it. Say a model
M verifies a formula A if A is true at all possible worlds in M. Say M
falsifies A if A is false at all. Note that in general A may be neither
verified nor falsified by M. Let T be the set of formulas verified by M, and
F the set falsified. Then T and F are disjoint, and for some models M there
are formulas which are in neither T nor F.
Introduce an appropriate coding from the formulas to the integers. Let T*
and F* be the sets of integers corresponding to the sets T and F for a given
Are T* and F* recursively separable, or effectively inseparable, or what?
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