The Universal Model for the Negation-free Fragment of IPC
Apostolos Tzimoulis, Zhiguang Zhao
Abstract:
We identify the universal n-model of the negation-free fragment of the
intuitionistic propositional calculus IPC. We denote it by U*(n) and
show that it is isomorphic to a generated submodel of the universal
n-model of IPC, which is denoted by U(n). We show that this close
resemblance makes U*(n) mirror many properties of U(n). Finally, using
U*(n), we give an alternative proof of Jankov's Theorem that the
intermediate logic KC, the logic of the weak excluded middle, is the
greatest intermediate logic extending IPC that proves exactly the same
negation-free formulas as IPC.