Classical subtheories and intuitionism

Abstract

By S we shall denote the set of all formulas in the language {—, &, V, and by C the classical consequence over S. The set of all theories we denote as Th. Th0 is the set of all theories T such that T = C(a), for some a e S. By Th1, we denote the set Th\Th0. The set of all complete theories we denote as Cpl. For a given T e Th let LT = {Y C T : Y e Th}. It is obvious that for every T e Th the system < LT, C> is a lattice. It is evident that in this lattice X U Y = C(X U Y) and X n Y = X A Y, for any X, Y e LT (Fragment tekstu).