Applied proof theory : proof interpretations and their use in mathematics
Ulrich Kohlenbach presents an applied form of proof theory that has led in recent years to new results in number theory, approximation theory, nonlinear analysis, geodesic geometry and ergodic theory (among others). This applied approach is based on logical transformations (so-called proof interpret...
Gorde:
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| Formatua: | Livre numérique |
| Hizkuntza: | Anglais |
| Argitaratua: |
Berlin ; Heidelberg :
Springer
[20..].
Cham : Springer Nature |
| Edizioa: | 1st ed. 2008. |
| Saila: | Springer Monographs in Mathematics
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| Gaiak: | |
| Sarrera elektronikoa: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Oharra: |
L'impression du document génère 538 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Applied proof theory, proof interpretations and their use in mathematics, U. Kohlenbach, 2008, Berlin, Springer, 1 vol. (XIX-532 p.), Springer monographs in mathematics, 978-3-540-77532-4 |
| Gaia: | Ulrich Kohlenbach presents an applied form of proof theory that has led in recent years to new results in number theory, approximation theory, nonlinear analysis, geodesic geometry and ergodic theory (among others). This applied approach is based on logical transformations (so-called proof interpretations) and concerns the extraction of effective data (such as bounds) from prima facie ineffective proofs as well as new qualitative results such as independence of solutions from certain parameters, generalizations of proofs by elimination of premises. The book first develops the necessary logical machinery emphasizing novel forms of Gödel's famous functional ('Dialectica') interpretation. It then establishes general logical metatheorems that connect these techniques with concrete mathematics. Finally, two extended case studies (one in approximation theory and one in fixed point theory) show in detail how this machinery can be applied to concrete proofs in different areas of mathematics |
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| Alearen deskribapena: | L'impression du document génère 538 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografia: | Bibliogr. Index |
| ISBN: | 9783540775331 |
| ISSN: | 2196-9922 |
| Sartu: | 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 |