Logic for Mathematicians

Intended for logicians and mathematicians, this text is based on Dr. Hamilton's lectures to third and fourth year undergraduates in mathematics at the University of Stirling. With a prerequisite of first year mathematics, the author introduces students and professional mathematicians to the techniques and principal results of mathematical logic. In presenting the subject matter without bias towards particular aspects, applications or developments, it is placed in the context of mathematics. To emphasize the level, the text progresses from informal discussion to the precise description and use of formal mathmematical and logical systems. The revision of this very successful textbook includes new sections on skolemization and the application of well-formed formulae to logic programming; numerous corrections have been made and extra exercises added. In Logic for Mathematicians, author Hamilton introduces the reader to the techniques and principle results of mathematical logic. Here is an introductory textbook which is designed to be useful not only to intending logicians but also to mathematicians in general. Based on Dr Hamilton's lectures to third and fourth year undergraduate mathematicians at the University of Stirling it has been written to introduce student or professional mathematicians, whose background need cover no more than a typical first year undergraduate mathematics course, to the techniques and principal results of mathematical logic.In presenting the subject matter without bias towards particular aspects, applications or developments, an attempt has been made to place it in the context of mathematics and to emphasise the relevance of logic to the mathematician. Starting at an elementary level, the text progresses from informal discussion to the precise description and use of formal mathematical and logical systems. The early chapters cover propositional and predicate calculus. The later chapters deal with Godel's theorem on the incompleteness of arithmetic and with various undecidability and unsolvability results, including a discussion of Turing machines and abstract computability.Each section ends with exercises designed to clarify and consolidate the material in that section. Hints or solutions to many of these are provided at the end of the book.The revision of this very successful textbook includes new sections on Skolemisation and applying well-formed formulas to logic programming. Some corrections have been made and extra exercises added. This is intended to introduce the student or professional mathematician to the techniques and principal results of mathematical logic. The text progresses from informal discussion to precise use of formal mathematical and logical systems. New sections include one on Skolemisation