Sets, Models and Proofs

 $29.99

 $29.99
Publisher Description
This textbook provides a concise and selfcontained introduction to mathematical logic, with a focus on the fundamental topics in firstorder logic and model theory. Including examples from several areas of mathematics (algebra, linear algebra and analysis), the book illustrates the relevance and usefulness of logic in the study of these subject areas.
The authors start with an exposition of set theory and the axiom of choice as used in everyday mathematics. Proceeding at a gentle pace, they go on to present some of the first important results in model theory, followed by a careful exposition of Gentzenstyle natural deduction and a detailed proof of Gödel’s completeness theorem for firstorder logic. The book then explores the formal axiom system of Zermelo and Fraenkel before concluding with an extensive list of suggestions for further study.
The present volume is primarily aimed at mathematics students who are already familiar with basic analysis, algebra and linear algebra. It contains numerous exercises of varying difficulty and can be used for selfstudy, though it is ideally suited as a text for a onesemester university course in the second or third year.