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Sets, Models and Proofs (Springer Undergraduate Mathematics Series) - Tapa blanda

Libro 72 de 90: Springer Undergraduate Mathematics

Moerdijk, Ieke; Van Oosten, Jaap

 
9783319924137: Sets, Models and Proofs (Springer Undergraduate Mathematics Series)
Tapa blanda
ISBN 10: 3319924133 ISBN 13: 9783319924137
Editorial: Springer, 2018

Sinopsis

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 Gödel’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.

"Sinopsis" puede pertenecer a otra edición de este libro.

Acerca del autor

Both authors have extensive experience in teaching the material covered in this book, and have been active researchers in mathematical logic and related fields. Ieke Moerdijk co-authored the influential Springer text  "Sheaves in Geometry and Logic, a First Course in Topos Theory", together with Saunders Mac Lane. Jaap van Oosten is an expert on realizability models for systems of constructive logic, and is the author of a comprehensive monograph on the subject: "Realizability: An Introduction to its Categorical Side" .

De la contraportada

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 Gödel’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.

"Sobre este título" puede pertenecer a otra edición de este libro.

Editorial
Springer
Año de publicación
2018
Idioma
Inglés
ISBN 10 
3319924133
ISBN 13 
9783319924137
Encuadernación
Tapa blanda
Número de edición
1
Número de páginas
156
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