A new semantics for intuitionistic predicate logic

Studia Logica 45 (1):9 - 17 (1986)
The main part of the proof of Kripke's completeness theorem for intuitionistic logic is Henkin's construction. We introduce a new Kripke-type semantics with semilattice structures for intuitionistic logic. The completeness theorem for this semantics can he proved without Henkin's construction.
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DOI 10.1007/BF01881545
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Intuitionistic Logic, Model Theory and Forcing.Melvin Fitting - 1969 - Amsterdam: North-Holland Pub. Co..

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