On 13 Mar 2013, at 17:37, Stephen P. King wrote:

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On 3/13/2013 12:22 PM, Bruno Marchal wrote:On 12 Mar 2013, at 18:54, Stephen P. King wrote:On 3/12/2013 12:22 PM, Bruno Marchal wrote:On 12 Mar 2013, at 14:10, Stephen P. King wrote:On 3/12/2013 8:58 AM, Stephen P. King wrote:Dear Bruno, I have found a paper that seems to cover most of my thoughts about the arithmetic body problem: Models of axiomatic theories admitting automorphisms by A. Ehrenfeucht A. Mostowski http://matwbn.icm.edu.pl/ksiazki/fm/fm43/fm4316.pdf More on related concepts are found in the Vaught conjecture: http://en.wikipedia.org/wiki/Vaught_conjecture"The topological Vaught conjecture is the statement thatwhenever aPolish group acts continuously on a Polish space, there areeithercountably many orbits or continuum many orbits. The topologicalVaughtconjecture is more general than the original Vaught conjecture: Given a countable language we can form the space of all structures on thenatural numbers for that language. If we equip this with thetopologygenerated by first order formulas, then it is known from A. Gregorczyk,A. Mostowski, C. Ryall-Nardzewski, "Definability of sets ofmodels ofaxiomatic theories", Bulletin of the Polish Academy of Sciences (seriesMathematics, Astronomy, Physics), vol. 9(1961), pp. 163–7 thattheresulting space is Polish. There is a continuous action of the infinitesymmetric group (the collection of all permutations of thenaturalnumbers with the topology of point wise convergence) which gives rise tothe equivalence relation of isomorphism. Given a complete firstordertheory T, the set of structures satisfying T is a minimal, closed invariant set, and hence Polish in its own right."Let me refine my concerns a bit. Is there a method to considertheVaught conjecture on finite lattice approximations of Polishspaces?Please relate all this, as formally as in the Ehrenfeucht Mostowski paper, to what has already been solved, in the ideal "toy" case ofsimple ideally correct machine, at the propositional level (thatis:the X, Z and S4Grz1) logics.There might be a way, but it sounds to me like a very difficultproblemfor expert in both provability logics and model theory. I thinkyou willneed the diagonal algebra of Magari.You will need to relate the work of the Italians, the Polish andtheGeorgians, hmm... That is a work for the Russians (the mathematicians!) :)I agree! ;-) Maybe there might already exist a solution in aRussianJournal now. I am trying to re-engage Pratt on this but I may haveto gofor alternatives, via Topos possibly.You can do that. The arithmetical topos is the one you can "extract" from the SGrz1 logic, by reversing the Boolos-Goldblatt morphism. Again the arithmetical topos will give the (non boolean) first personpicture only. The inner god, or the universal, in Plotinus term.Thisis only 1/8 of the comp global picture. But it is important. AsPlotinusunderstood, the soul as already a foot in matter, and the S4Grz1logicis already quantum-like.Hi Bruno, Nice, so to find more people that understand what a Boolos-Goldblattmorphism is and how to reverse it *and* how it might be parametrizedismy mission.

`They need to have read my work, as S4Grz is not enough, you need`

`S4Grz1, and thus the sigma_1 restriction, and thus UDA and the comp`

`mind body problem.`

Bruno

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