Hi Aditya, Le 06-août-05, à 00:19, Aditya Varun Chadha a écrit :

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Greetings, Not sure of the exact formal meaning but I think Bruno is talking something related to Godel's incompleteness for second order and "higher" logics. (sorry if that was already obvious)

`G and G* do not really depend on the logical order of the`

`theory/machine concerned, as far as the proofs given by the machine are`

`mechanically checkable.`

Of course provability can obey universal principles: for example the notion of classical checkable proof in sufficiently rich system is completely captured by the modal logics G and G*.Well, you lost me on that one! Hal FinneyI'd guess that this can be translated into the computability problem (problems of the class of HALTING) for the Universal TM. i.e. "Reachability" in ANY Turing Machine is limited to "sub-HALTING" problems (very very vague and informal on my part).

I would say "reachability" = "halting".

The church turing thesis also is infact a statement about computability in the universal sense, independant of the model of computation used.

Yes.

Or maybe I am totally off, in that case, sorry for blabbering without reading up what "modal logics G and G*" exactly are.

I will come back on this. Meanwhile you can read my posts: http://www.escribe.com/science/theory/m1417.html http://www.escribe.com/science/theory/m2855.html or better my paper available here:

`http://iridia.ulb.ac.be/~marchal/publications/`

`SANE2004MARCHALAbstract.html`

`It gives a description of Solovay's theorem which makes the link`

`between the modal logic G and G* and the Godel Lob incompleteness`

`theorems.`

Bruno http://iridia.ulb.ac.be/~marchal/