Abstract

The infinitary languages studied in this book are those in which quantification of infinitely many variables simultaneously, and conjunctions or alternations of infinitely many are permitted. Infinitary concatenation and infinitary propositional logics are first discussed, and a completeness theorem is proved about the latter. The later chapters deal with infinitary predicate languages and Scott's proof of incompleteness is introduced. Throughout the discussion, unsolved problems are mentioned and areas undergoing current development are emphasized. A short bibliography lists most recent articles on this new branch of logic.—P. J. M.