On the independence of premiss axiom and rule

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Archive for Mathematical Logic 59 (7-8):793-815 (2020)
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Abstract

In this paper, we deal with a relationship among the law of excluded middle, the double negation elimination and the independence of premiss rule ) for intuitionistic predicate logic. After giving a general machinery, we give, as corollaries, several examples of extensions of \ and \ which are closed under \ but do not derive the independence of premiss axiom.

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10.1007/s00153-019-00707-5

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References found in this work

Constructivism in mathematics: an introduction.A. S. Troelstra - 1988 - New York, N.Y.: Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.. Edited by D. van Dalen.
The foundations of intuitionistic mathematics.Stephen Cole Kleene - 1965 - Amsterdam,: North-Holland Pub. Co.. Edited by Richard Eugene Vesley.
Realizability.A. S. Troelstra - 2000 - Bulletin of Symbolic Logic 6 (4):470-471.
Finite sets and infinite sets in weak intuitionistic arithmetic.Takako Nemoto - 2020 - Archive for Mathematical Logic 59 (5-6):607-657.

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