Abstract

This extensive work is both a systematization of past developments, and an extension to new areas, of the application of mathematical apparatus to the study of logical systems; it does not aim to include all such metamathematical devices, Gödel-numbering for example, but to emphasize algebraic and topological ones. The first part surveys required algebraic and topological notions; in the second part they are applied to classical logic—propositional and predicate calculi; in the final section, modal and intuitionistic, non-classical logics come under scrutiny. The reader should come prepared with a working knowledge of the forementioned areas of mathematics; but the pace is leisurely, and the book tries to be self-contained. It succeeds admirably and may become the standard examination of the topic.—P. J. M.