On 3/12/2013 1:54 PM, Stephen P. King wrote:
>> Let me refine my concerns a bit. Is there a method to consider the
>> >> Vaught conjecture on finite lattice approximations of Polish spaces?
>>
>> Please relate all this, as formally as in the Ehrenfeucht Mostowski
>> paper, to what has already been solved, in the ideal "toy" case of
>> simple ideally correct machine, at the propositional level (that is:
>> the X, Z and S4Grz1) logics.
>>
>> There might be a way, but it sounds to me like a very difficult problem
>> for expert in both provability logics and model theory. I think you will
>> need the diagonal algebra of Magari.

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Hi Bruno,
I am looking at
http://www.encyclopediaofmath.org/index.php/Magari_algebra reference of
Magari algebra. I see the nice relation to the Stone compactum and even
a definition that looks like bisimulation:
http://www.encyclopediaofmath.org/legacyimages/m/m110/m110020/m11002055.png
which, I suspect, is necessary to model interactions between the observers.
I suspect that we need to look at the associativity properties of the
algebra as per Kevin Knuth's work: http://arxiv.org/abs/1209.0881
--
Onward!
Stephen
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