A Course in Mathematical Logic for Mathematicians
A Course in Mathematical Logic for Mathematicians, Second Edition offers a straightforward introduction to modern mathematical logic that will appeal to the intuition of working mathematicians. The book begins with an elementary introduction to formal languages and proceeds to a discussion of proof...
Kaydedildi:
| Yazar: | |
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| Materyal Türü: | Livre numérique |
| Dil: | Anglais |
| Baskı/Yayın Bilgisi: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edisyon: | 2nd ed. 2010. |
| Seri Bilgileri: | Graduate Texts in Mathematics
53 |
| Online Erişim: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Not: |
Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • A course in mathematical logic for mathematicians, Yu. I. Manin, 2nd edition, 2010, New York [etc.], Springer, 1 vol. (XVII-384 p.), Graduate texts in mathematics, 978-1-4419-0614-4 • A Course in Mathematical Logic for Mathematicians, Texte imprimé, 9781441906168 • A course in mathematical logic for mathematicians, Yu. I. Manin, 2nd edition, 2010, New York [etc.], Springer, 1 vol. (XVII-384 p.), Graduate texts in mathematics, 978-1-4419-0614-4 • A Course in Mathematical Logic for Mathematicians, Texte imprimé, 9781461424796 |
| Özet: | A Course in Mathematical Logic for Mathematicians, Second Edition offers a straightforward introduction to modern mathematical logic that will appeal to the intuition of working mathematicians. The book begins with an elementary introduction to formal languages and proceeds to a discussion of proof theory. It then presents several highlights of 20th century mathematical logic, including theorems of Gödel and Tarski, and Cohen's theorem on the independence of the continuum hypothesis. A unique feature of the text is a discussion of quantum logic. The exposition then moves to a discussion of computability theory that is based on the notion of recursive functions and stresses number-theoretic connections. The text present a complete proof of the theorem of Davis Putnam Robinson Matiyasevich as well as a proof of Higman's theorem on recursive groups. Kolmogorov complexity is also treated. Part III establishes the essential equivalence of proof theory and computation theory and gives applications such as Gödel's theorem on the length of proofs. A new Chapter IX, written by Yuri Manin, treats, among other things, a categorical approach to the theory of computation, quantum computation, and the P/NP problem. A new Chapter X, written by Boris Zilber, contains basic results of model theory and its applications to mainstream mathematics. This theory has found deep applications in algebraic and diophantine geometry. Yuri Ivanovich Manin is Professor Emeritus at Max-Planck-Institute for Mathematics in Bonn, Germany, Board of Trustees Professor at the Northwestern University, Evanston, IL, USA, and Principal Researcher at the Steklov Institute of Mathematics, Moscow, Russia. Boris Zilber, Professor of Mathematical Logic at the University of Oxford, has contributed the Model Theory Chapter for the second edition |
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| Diğer Bilgileri: | Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| ISBN: | 9781441906151 |
| ISSN: | 2197-5612 |
| Erişim: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |