From intuitionism to many-valued logics through Kripke models (Q2658284)

Intuitionistic propositional logic was proved to be an infinitely many valued logic by [\textit{K. Gödel}, Collected works. Volume I: Publications 1929--1936. Ed. by Solomon Feferman et al. New York: Oxford University Press; Oxford: Clarendon Press (1986; Zbl 0592.01035)], and it is proved by \textit{S. Jaskowski} [Actual. Sci. Ind. 393, 58--61 (1936; JFM 62.1045.07)] to be a countably many valued logic. The current paper provides alternative proofs for these theorems using models of \textit{S. A. Kripke} [J. Symb. Log. 24, 1--14 (1959; Zbl 0091.00902)]. Gödel's proof gave rise to an intermediate propositional logic (between intuitionistic and classical), that is known nowadays as Gödel or the Gödel-Dummett Logic, and is studied by fuzzy logicians as well. Some results on the inter-definability of propositional connectives in this logic are presented. For the entire collection see [Zbl 1459.03003].