Publisher： Cambridge University Press
E-ISSN： 1943-5886|49|4|1339-1349
ISSN： 0022-4812
Source： The Journal of Symbolic Logic, Vol.49, Iss.4, 1984-12, pp. : 1339-1349
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Abstract
Among the more traditional semantics for intuitionistic logic the Beth and the Kripke semantics seem well-suited for direct manipulations required for the derivation of metamathematical results. In particular Smoryński demonstrated the usefulness of Kripke models for the purpose of obtaining closure properties for first-order arithmetic, [S], and second-order arithmetic, [J-S]. Weinstein used similar techniques to handle intuitionistic analysis, [W]. Since, however, Beth-models seem to lend themselves better for dealing with analysis, cf. [D], we have developed a somewhat more liberal semantics, that shares the features of both Kripke and Beth semantics, in order to obtain analogues of Smoryński's
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