An Invitation to Mathematical Logic

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Sprache: Englisch

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Beschreibung

In addition to covering the essentials, the author's intention in writing this text is to entice the reader to further study mathematical logic. There is no current "standard text" for a first graduate course in mathematical logic and this book will fill that gap. While there is more material than could be covered in a traditional one semester course, an instructor can cover the basics and still have the flexibility to choose several weeks' worth of interesting advanced topics that have been introduced. The text can and will be used by people in various courses with different sorts of perspectives. This versatility is one of the many appealing aspects of this book. A list of suggested portions to be covered in a single course is provided as well as a useful chart which maps chapter dependencies. Additionally, a motivated student will have ample material for further reading.

New definitions, formalism, and syntax have been streamlined to engage the reader quickly into the heart of logic and to more sophisticated topics. Part I and Part IV center on foundational questions, while Part III establishes the fundamentals of computability. Part II develops model theory, highlighting the model theory of the fields of real and complex numbers. The interplay between logic and other areas of mathematics, notably algebra, number theory, and combinatorics, are illustrated in Chapters 5, 6, 8, 14, and 16. For most of the text, the only prerequisite is mathematical maturity. The material should be accessible to first year graduate students or advanced undergraduates in mathematics, graduate students in philosophy with a solid math background, or students in computer science who want a mathematical introduction to logic. Prior exposure to logic is helpful but not assumed.

Über den Autor

David Marker is Professor Emeritus of Mathematics at the University of Illinois at Chicago where he was Liberal Arts & Sciences Distinguished Professor and a Fellow of the American Mathematical Society. His research interests lie in model theory and its applications. His textbook, Model Theory: An Introduction, which appeared as GTM 217 in 2002, was awarded the Association of Symbolic Logic Shoenfield Prize for expository writing.

Inhaltsverzeichnis

Introduction.- I. Truth and Proof.- 1 Languages, Structures and Theories.- 2 Embeddings and Substructures.- 3 Formal Proofs.- 4 Gödel's Completeness Theorem.- II. Elements of Model Theory.- 5 Compactness and Complete Theories.- 6 Ultraproducts.- 7 Quantifier Elimination.- 8 Model Theory of the Real Field.- III. Computability.- 9 Models of Computation.- 10 Universal Machines and Undecidability.- 11 Computably Enumerable and Arithmetic Sets.- 12 Turing Reducibility.- IV. Arithmetic and Incompleteness.-13 Gödel's Incompleteness Theorems.- 14 Hilbert's 10th Problem.- 15 Peano Arithmetic and ¿0.- 16 Models of Arithmetic and Independence Results. - Appendices.- A Set Theory. - B Unique Readability. - C Real Algebra. -Bibliography. - Index.

Details

Erscheinungsjahr:	2025
Fachbereich:	Grundlagen
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xviii 357 S. 7 s/w Illustr. 357 p. 7 illus.
ISBN-13:	9783031553707
ISBN-10:	3031553705
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Marker, David
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 20 mm
Von/Mit:	David Marker
Erscheinungsdatum:	08.05.2025
Gewicht:	0,638 kg

Artikel-ID: 133188526

Über den Autor

Inhaltsverzeichnis

Details

Erscheinungsjahr:	2025
Fachbereich:	Grundlagen
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xviii 357 S. 7 s/w Illustr. 357 p. 7 illus.
ISBN-13:	9783031553707
ISBN-10:	3031553705
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Marker, David
Hersteller:	Springer Nature Switzerland Springer International Publishing Springer International Publishing AG
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 20 mm
Von/Mit:	David Marker
Erscheinungsdatum:	08.05.2025
Gewicht:	0,638 kg