  Intuitionistic Propositional Logic is proved to be an infinitely many valued
logic by Kurt G\"odel (1932), and it is proved by Stanis{\l}aw Ja\'skowski
(1936) to be a countably many valued logic. In this paper, we provide
alternative proofs for these theorems by using models of Saul Kripke (1959).
G\"odel's proof gave rise to an intermediate propositional logic (between
intuitionistic and classical), that is known nowadays as G\"odel or the
G\"odel-Dummet Logic, and is studied by fuzzy logicians as well. We also
provide some results on the inter-definablility of propositional connectives in
this logic.
