Artemov, S., Explicit provability and constructive semantics. Bull. Symbolic Logic 7, pp. 1-36 (2001).  Home/Search   Document Details and Download   Summary   Related Articles

....use this to show that there are infinitely many primes. Use this proof to obtain an upper bound g(j) for the next prime p j 1 as in the 3. proof of this statement above. Can you improve the bound we obtained from the latter (see Hacks [52] 2) Let (a n ) n#IN be a sequence of rational numbers in [0, 1] with #n # IN(a n 1 # a n ) Since rational numbers can be coded by natural numbers one can consider (a n ) as a number theoretic function. The order relation # and the usual arithmetical operations between rational numbers are primitive recursive in their codes. Construct a primitive ....

....a so called logic of proofs where proof in the BHK clauses is interpreted as t is a proof (polynomial) for A referring to some standard proof (not: provability) predicate e.g. for PA. Using this interpretation he proves a completeness result for intuitionistic propositional logic (see [1]) Intuitionistic ( Heyting )arithmetic HA L(HA) contains the logical constants of L(IL) number variables x, y, z, a constant 0 (zero) a unary function constant S (successor) function constants for all primitive recursive functions (more precisely for all derivations of primitive ....

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Artemov, S., Explicit provability and constructive semantics. Bull. Symbolic Logic 7, pp. 1-36 (2001).

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