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Markov's Rule revisited
Archive for Mathematical Logic 30 (2):125-127 (1990)
Abstract
We consider HA*, that is Heyting's Arithmetic extended with transfinite induction over all recursive well orderings, which may be viewed as defining constructive truth, since PA* agrees with classical truth. We prove that Markov's Principle, as a schema, is not provable in HA*, but that HA* is closed under Markov's Rule.Author's Profile
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Citations of this work
Markov’s Principle and Subsystems of Intuitionistic Analysis.Joan Rand Moschovakis - 2019 - Journal of Symbolic Logic 84 (2):870-876.
The logic of Brouwer and Heyting.Joan Rand Moschovakis - 2009 - In Dov Gabbay, The Handbook of the History of Logic. Elsevier. pp. 77-125.
References found in this work
Proof theory and constructive mathematics.Anne S. Troelstra - 1977 - In Jon Barwise, Handbook of mathematical logic. New York: North-Holland. pp. 973--1052.
Absoluteness of intuitionistic logic.Daniel Maurice Raphaël Leivant - 1979 - Amsterdam: Mathematisch Centrum.
Constructivism in Mathematics, Volume 2.A. S. Troelstra & D. van Dalen - 1991 - Studia Logica 50 (2):355-356.
On the Consistency of Certain Logical Calculus.P. S. Novikoff - 1946 - Journal of Symbolic Logic 11 (4):129-131.
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