A. N. Kolmogorov. On the principle of the excluded middle (russian). Mat. Sb., 32:646--667, 1925. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Proof Interpretations and the Computational Content of Proofs - Kohlenbach (2002) (1 citation) (Correct)
....variant. All these translations A ## A # have in common that A # is (or is intuitionistically equivalent to) a negative formula. The first such translation is due to Godel [44] although G. Gentzen independently discovered a similar translation) There is some preceding work by Kolmogorov [88] and Glivenko [41] Two further variants of Godel s translation are due to Kuroda [99] and it his one of these which we will adopt here: Definition 7.1 Let A be a formula in a theory based on L(IL # ) A # is defined as A # :# A # , where A # is defined by induction on the logical structure ....
Kolmogorov, A.N., On the principle of the excluded middle (Russian). Mat. Sb. 32, pp.646-667 (1925).
On the computational content of the Axiom of Choice - Berardi, Bezem, Coquand (1995) (8 citations) (Correct)
....we can prove indeed that r OE follows from OE; and r from r OE and OE ) r : Since absurdity is not interpreted by the empty type, we cannot realize ) OE for all OE. We overcome this problem by exercising some care in the negative interpretation. The idea is essentially due to Kolmogorov [13]. We employ the fact that ) r OE can be proved for all OE without using the axiom schema ) OE. Although our prime formulae are decidable, the negative interpretation of a prime formula OE will be r OE. As negative interpretation we use a standard version of the double negation translation, i.e. ....
A.N. Kolmogorov. On the principle of the excluded middle. In From Frege to Godel, J. van Heijenoort, editor, Harvard University Press, Cambridge MA, 1971, pp. 414-437.
The Kolmogorov Interpretation of Classical Logic in Intuitionistic .. - Brown (1998) Self-citation (Kolmogorov) (Correct)
....of two metatheorems (soundness and completeness of the interpretation) are represented as higher level judgments. These proofs are also implemented in Twelf. In 1925, Kolmogorov showed how to interpret classical logic in intuitionistic logic using a double negation translation of formulas (see [Kol67]) Kolmogorov worked with a Hilbert style axiomatization of classical logic and intuitionistic logic (using only implication and negation for the propositional case) Actually, Kolmogorov s axiomatization of intuitionistic logic gives only the minimal calculus. In this report, we work with ....
A. Kolmogorov. On the principle of excluded middle. In From Frege to Godel, pages 414--437. Harvard University Press, 1967.
Proof Mining in Subsystems of Analysis - Oliva (2003) (Correct)
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A. N. Kolmogorov. On the principle of the excluded middle (russian). Mat. Sb., 32:646--667, 1925.
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