This book gives a mathematical treatment of the basic ideas and results of logic. It is intended to serve as a textbook for an introductory mathematics course in logic at the junior-senior level. The objectives are to present the important concepts and theorems of logic and to explain their significance and their relationship to the reader's other mathematical work.

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Computability Theory: An Introduction to Recursion Theory provides a concise, comprehensive, and authoritative introduction to contemporary computability theory, techniques, and results. The basic concepts and techniques of computability theory are placed in their historical, philosophical and logical context. This presentation is characterized by an unusual breadth of coverage and the inclusion of advanced topics not to be found elsewhere in the literature at this level. The text includes both the standard material for a first course in computability and more advanced looks at degree structures, forcing, priority methods, and determinacy. The final chapter explores a variety of computability applications to mathematics and science. Computability Theory is an invaluable text, reference, and guide to the direction of current research in the field. Nowhere else will you find the techniques and results of this beautiful and basic subject brought alive in such an approachable way. - Frequent historical information presented throughout - More extensive motivation for each of the topics than other texts currently available - Connects with topics not included in other textbooks, such as complexity theory

Abraham (Abram) Joseph Warner was born in Connecticut in 1821 to Ard and Mary (Bronson) Warner, Jr. Abraham married in 1854 Emily Benson who died in 1855. He married his second wife, Frances Louisa Bishop, in 1855 in Indiana. He graduated from Trinity College, Hartford, Connecticut, in 1842; tutored at Jubilee College in 1842-1845; was an Episcopal missionary in Sterling, Illinois, and its vicinity during 1845-1850; ordained a priest in 1847; established St. Peter's Episcopal Church in Grand Detour, Illinois in 1850; was a chaplain to the 12th Illinois Cavalry Regiment during the Civil War, serving mainly in Virginia; and was rector at Boardman, Ohio, in 1864, and of St. Paul's Episcopal Church of Angelica, New York, 1881-1885.

本書は、アメリカの大学の数学科において広く採用されている、標準的な数理論理学のテキストの翻訳です。数理論理学の基本定理である1階論理の完全性定理、ゲーデルの不完全性定理(第1および第2)の完全な証明に加え、完全性定理の応用例としての超準解析、2階論理の初歩までをカバーしています。