Elements of Intuitionism

This first introduction to intuitionistic mathematics concentrates on the fundamental concepts, leading the reader step-by-step through the subject. After a preliminary philosophical orientation, and a sketch of the differences between intuitionistic and classical reasoning, the author outlines the intuitionistic approach to the theory of real numbers. This gives the reader a taste of intuitionistic maths, to motivate the following discussion of the foundations. This begins with the intuitionistic analysis concepts of choice sequences and spreads, and the bar-induction and continuity principles which govern them. The author then gives a much-needed discussion of first-order intuitionistic logic from both proof-theoretic aspect and as handled semantically by Beth and Kripke trees. The section finishes with a comprehensive survey of results concerning the completeness of intuitionistic logic. in detail. The book goes on to look at some metamathematical results, realizability, and at the theory of the creative subject, and ends with an analysis of the philosophical issues. Students of mathematics, logic and philosophy.