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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Constructivism in Mathematics: An Introduction.A. S. Troelstra & Dirk Van Dalen - 1988 - Amsterdam: North Holland. Edited by D. van Dalen.
Realizability.A. S. Troelstra - 2000 - Bulletin of Symbolic Logic 6 (4):470-471.
A note on the independence of premiss rule.Hajime Ishihara & Takako Nemoto - 2016 - Mathematical Logic Quarterly 62 (1-2):72-76.

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