Abstract

Within a weak system $${{{\sf WKVS}}}$$WKVS of intuitionistic analysis one may prove, using the Weak Fan Theorem as an additional axiom, a completeness theorem for intuitionistic first-order predicate logic relative to validity in generalized Beth models as well as a completeness theorem for classical first-order predicate logic relative to validity in intuitionistic structures. Conversely, each of these theorems implies over $${{{\sf WKVS}}}$$WKVS the Weak Fan Theorem.

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