Comments on: Kreisel’s No-Counterexample Interpretation: How can we turn proofs in elementary number theory into programs? http://xorshammer.com/2008/08/13/kreisels-no-counterexample-interpretation/ Some things in mathematical logic that I find interesting Sat, 03 Mar 2012 11:53:40 +0000 hourly 1 http://wordpress.com/ By: Sequential compactness theorem @ unwanted capture http://xorshammer.com/2008/08/13/kreisels-no-counterexample-interpretation/#comment-194 Sun, 14 Jun 2009 21:54:53 +0000 http://xorshammer.wordpress.com/?p=19#comment-194 [...] Kohlenbach in the comments on the post, the finite convergence principle is nothing more than the no-counterexample interpretation of the infinite convergence principle. (See this paper by Kohlenbach and Gaspar for more details.) [...]

]]> By: François Dorais http://xorshammer.com/2008/08/13/kreisels-no-counterexample-interpretation/#comment-21 Sun, 17 Aug 2008 19:18:16 +0000 http://xorshammer.wordpress.com/?p=19#comment-21 I always liked the game-theoretic interpretation of Kreisel’s No-Counterexample Interpretation (and its big brother, Gödel’s Dialectica). This is related to the semantics game described in my post on Fraïssé’s Theorem.

The witnessing functions form (the main part of) a winning strategy for True in the semantics game. While True’s winning strategy in that game is not computable in general, Kreisel’s No-Counterexample Interpretation says that there is a computable functional that witnesses that False does not have winning strategy in the semantics game associated to a true statement. Consequently, the existence of witnessing functions is equivalent to some form of determinacy (which depends on the base axioms).

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