Hi Marchal, This is a reply to your last two posts. I hope other everythingers beside myself are attempting to follow this adventure in logic. It appears to be really worth the effort. Please feel free to contribute to this exchange.
Marchal wrote: And we have as results (including the exercices!): > Any frame (W,R) respects K >A frame (W,R) respects T iff R is reflexive >A frame (W,R) respects 4 iff R is transitive >A frame (W,R) respects 5 iff R is euclidian > (where R is Euclidian means that if xRy and xRz then yRz, for x, y z in W). >A frame (W,R) respects D iff (W,R) is ideal >A frame (W,R) respects C iff (W,R) is realist. >We will talk on the semantics of L and Grz later. I do not think you defined euclidian.... There is obviously a connection to geometry but I dn't see it. > Actually we will need also > > -Predicate logic, and arithmetics > -weak logics (intuitionist logic, quantum logic) > -Algebraic semantics of weak logics > -Kripke semantics of weak logics > I guess we have to visit the whole Louvre to get to the Mona Lisa :-). Any short cut? > Then the interview itself will begin. We can follow the historical > progress of that interview: > > -Goedel's theorem; > -Loeb's theorem; (just this one makes the travel worth!) > -Solovay's theorem; > -Muravitski & Kusnetsov, Boolos, Goldblatt theorems; > -Other theorems by Goldblatt > -Still Other theorems by Goldblatt. > -Visser's theorem; > > It is the theorem by Solovay which will make clear the relation > between provability logic and some modal logics. > Boolos, Goldblatt, Visser has found result which will make part > of our the translation of the UDA argument almost transparent. Thank you for outlining a itinirary for our journey into logic.... I thought our destination was much closer.. Does it have to be that complicated? Thanks for the effort. George
