Validity and quantification in intuitionism

Journal of Philosophical Logic 10 (1):117 - 126 (1981)
We distinguish three different readings of the intuitionistic notions of validity, soundness, and completeness with respect to the quantification occurring in the notion of validity, and we establish certain relations between the different readings. For each of the meta-logicalnotions considered we suggest that the "most natural" reading (which is not the same for all cases) is precisely the one which is required by the recent intuitionistic completeness theorems for IPC
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DOI 10.1007/BF00253915
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A. Heyting (1971). Intuitionism. Amsterdam,North-Holland Pub. Co..

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