The first-order logic of CZF is intuitionistic first-order logic

Journal of Symbolic Logic 89 (1):308-330 (2024)
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Abstract

We prove that the first-order logic of CZF is intuitionistic first-order logic. To do so, we introduce a new model of transfinite computation (Set Register Machines) and combine the resulting notion of realisability with Beth semantics. On the way, we also show that the propositional admissible rules of CZF are exactly those of intuitionistic propositional logic.

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10.1017/jsl.2022.51

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Robert Passmann
University of Amsterdam

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References found in this work

Constructivism in Mathematics, An Introduction.A. Troelstra & D. Van Dalen - 1991 - Tijdschrift Voor Filosofie 53 (3):569-570.
Foundations of Set Theory.A. A. Fraenkel, Y. Bar Hillel & A. Levy - 1975 - British Journal for the Philosophy of Science 26 (2):165-170.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (25-30):461-461.
Choice Implies Excluded Middle.N. Goodman & J. Myhill - 1978 - Mathematical Logic Quarterly 24 (25‐30):461-461.

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