Negationless intuitionism |
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Authors: | Martino Enrico |
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Affiliation: | (1) Dipartimento di Matematica, Universitá di Padova, Via Belzoni 7, I-35131 Padova, Italy |
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Abstract: | The present paper deals with natural intuitionistic semantics for intuitionistic logic within an intuitionistic metamathematics. We show how strong completeness of full first order logic fails. We then consider a negationless semantics à la Henkin for second order intuitionistic logic. By using the theory of lawless sequences we prove that, for such semantics, strong completeness is restorable. We argue that lawless negationless semantics is a suitable framework for a constructive structuralist interpretation of any second order formalizable theory (classical or intuitionistic, contradictory or not). |
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