Provability, Computability and Reflection.

This paper lays out a program for analysing relevance constructively. It begins with a summary of results concerning the system C of Pottinger [197a] which has entailment, relevant implication, S4 strict implication, and intuitionist implication among its connectives. A full working out of the motivation for C will require formal analysis of informal concepts derived from the usual explanation of the meanings of the constants of intuitionist propositional logic. Formal machinery which should be adequate for the proof theoretic side of (...) the analysis of the nonmodal part of C is described in detail, and the direction in which semantical results are to be sought is indicated. (shrink)

The main aim of Schonfinkel's paper was methodological: to reduce the primitive logical notions to as few and definite notions as possible. ...

This is a long-awaited new edition of one of the best known Oxford Logic Guides. The book gives an introduction to intuitionistic mathematics, leading the reader gently through the fundamental mathematical and philosophical concepts. The treatment of various topics, for example Brouwer's proof of the Bar Theorem, valuation systems, and the completeness of intuitionistic first-order logic, have been completely revised.