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Abstract: We find a complete axiomatization of the logic LP of propositions and proofs anticipated by Kolmogorov and Gödel. We apply LP to solve two closely related problems. In 1933 Gödel introduced a calculus of provability (also known as modal logic S4) and left open the question of its exact intended semantics. We give a solution to this problem by showing that Godel's provability calculus is nothing but the forgetful projection of LP. This also achieves Godel's objective of defining intuitionistic... (Update)
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...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...
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BibTeX entry: (Update)
Artemov, S., Explicit provability and constructive semantics. Bull. Symbolic Logic 7, pp. 1-36 (2001). http://citeseer.ist.psu.edu/artemov00explicit.html More
@article{ artemov00explicit,
author = "Sergei N. Artemov",
title = "Explicit Provability and Constructive Semantics",
journal = "The Bulletin of Symbolic Logic",
volume = "7",
number = "1",
pages = "1--36",
year = "2000",
url = "citeseer.ist.psu.edu/artemov00explicit.html" }
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