69,54 €*
Versandkostenfrei per Post / DHL
Aktuell nicht verfügbar
This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel's classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel's second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo's axioms, containing a presentation of Gödel's constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers.
The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel's classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel's second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo's axioms, containing a presentation of Gödel's constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers.
The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.
| Fachbereich: | Grundlagen |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| ISBN-13: | 9783030522780 |
| ISBN-10: | 3030522784 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-030-52278-0 |
| Autor: |
Halbeisen, Lorenz
Krapf, Regula |
| Hersteller: |
Birkhäuser
Springer, Berlin Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Heidelberg, Tiergartenstr. 17, D-69121 Heidelberg, buchhandel-buch@springer.com |
| Abbildungen: | XII, 236 p. |
| Maße: | 19 x 161 x 245 mm |
| Von/Mit: | Lorenz Halbeisen (u. a.) |
| Erscheinungsdatum: | 17.10.2020 |
| Gewicht: | 0,496 kg |
| Fachbereich: | Grundlagen |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| ISBN-13: | 9783030522780 |
| ISBN-10: | 3030522784 |
| Sprache: | Englisch |
| Herstellernummer: | 978-3-030-52278-0 |
| Autor: |
Halbeisen, Lorenz
Krapf, Regula |
| Hersteller: |
Birkhäuser
Springer, Berlin Springer International Publishing |
| Verantwortliche Person für die EU: | Springer Heidelberg, Tiergartenstr. 17, D-69121 Heidelberg, buchhandel-buch@springer.com |
| Abbildungen: | XII, 236 p. |
| Maße: | 19 x 161 x 245 mm |
| Von/Mit: | Lorenz Halbeisen (u. a.) |
| Erscheinungsdatum: | 17.10.2020 |
| Gewicht: | 0,496 kg |
Ähnliche Produkte
Lieferzeit 2-4 Werktage
Lieferzeit 1-2 Wochen
Lieferzeit 2-4 Werktage
Lieferzeit 2-4 Werktage
Lieferzeit 1-2 Werktage
Lieferzeit 1-2 Wochen
