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Sets, Models and Proofs (Paperback, 1st ed. 2018)
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Sets, Models and Proofs (Paperback, 1st ed. 2018)
Series: Springer Undergraduate Mathematics Series
Expected to ship within 10 - 15 working days
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This textbook provides a concise and self-contained introduction to
mathematical logic, with a focus on the fundamental topics in
first-order 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 Gentzen-style natural deduction and a detailed proof
of Goedel's completeness theorem for first-order 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 self-study, though it is ideally
suited as a text for a one-semester university course in the second
or third year.
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