Modern Mathematical Logic

AvJoseph Mileti

Inbunden, Engelska, 2022

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Beskrivning

This textbook gives a complete and modern introduction to mathematical logic. The author uses contemporary notation, conventions, and perspectives throughout, and emphasizes interactions with the rest of mathematics. In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions to the pillars of the modern subject: model theory, set theory, and computability. Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level. Numerous examples reinforce the key ideas and illustrate their applications, and a wealth of classroom-tested exercises serve to consolidate readers' understanding. Comprehensive and engaging, this book offers a fresh approach to this enduringly fascinating and important subject.

Produktinformation

Utgivningsdatum:2022-09-22
Mått:185 x 260 x 35 mm
Vikt:1 160 g
Format:Inbunden
Språk:Engelska
Serie:Cambridge Mathematical Textbooks
Antal sidor:518
Förlag:Cambridge University Press
ISBN:9781108833141

Utforska kategorier

Mer om författaren

Joseph Mileti is Associate Professor in the Department of Mathematics and Statistics at Grinnell College, USA. He won the 2004 Sacks Prize from the Association of Symbolic Logic for the best doctoral dissertation in mathematical logic (worldwide) and leading experts have celebrated his original courses and materials taught at many universities.

Recensioner i media

'This is an excellent introduction to mathematical logic for upper-year undergraduate students with some background in theoretical mathematics. The many wonderful examples relate mathematical logic to other areas of mathematics. Beyond the usual setup and culmination with completeness and incompleteness, Mileti gives a strong introduction to set theory, model theory, and computability. Instructors have the flexibility to suit the examples and direction to their students' backgrounds, and curious students will have an excellent reference for topics not covered in their course. Mileti's gentle prose guides the reader from topic to topic, explaining what we are doing, and why.' Barbara F. Csima, University of Waterloo

Innehållsförteckning

Preface; Acknowledgements; 1. Introduction; 2. Induction and recursion; 3. Propositional logic; 4. First-order logic: languages and structures; 5. Relationships between structures; 6. Implication and compactness; 7. Model theory; 8. Axiomatic set theory; 9. Ordinals, cardinals, and choice; 10. Set-theoretic methods in model theory; 11. Computable sets and functions; 12. Logic, computation, and incompleteness; Appendix: mathematical background; References; Index.