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03671nam a22005295i 4500 |
| 001 - CONTROL NUMBER |
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| control field |
978-3-540-77533-1 |
| 003 - CONTROL NUMBER IDENTIFIER |
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| control field |
DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION |
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20161121231215.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION |
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cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION |
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100301s2008 gw | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER |
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| International Standard Book Number |
9783540775331 |
| -- |
978-3-540-77533-1 |
| 024 7# - OTHER STANDARD IDENTIFIER |
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| Standard number or code |
10.1007/978-3-540-77533-1 |
| Source of number or code |
doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER |
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| Classification number |
QA8.9-10.3 |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBC |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
PBCD |
| Source |
bicssc |
| 072 #7 - SUBJECT CATEGORY CODE |
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| Subject category code |
MAT018000 |
| Source |
bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER |
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| Classification number |
511.3 |
| Edition number |
23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME |
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| Personal name |
Kohlenbach, Ulrich. |
| Relator term |
author. |
| 245 10 - TITLE STATEMENT |
|---|
| Title |
Applied Proof Theory: Proof Interpretations and Their Use in Mathematics |
| Medium |
[electronic resource] / |
| Statement of responsibility, etc. |
by Ulrich Kohlenbach. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE |
|---|
| Place of production, publication, distribution, manufacture |
Berlin, Heidelberg : |
| Name of producer, publisher, distributor, manufacturer |
Springer Berlin Heidelberg, |
| Date of production, publication, distribution, manufacture, or copyright notice |
2008. |
| 300 ## - PHYSICAL DESCRIPTION |
|---|
| Extent |
XX, 536 p. |
| Other physical details |
online resource. |
| 336 ## - CONTENT TYPE |
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| Content type term |
text |
| Content type code |
txt |
| Source |
rdacontent |
| 337 ## - MEDIA TYPE |
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| Media type term |
computer |
| Media type code |
c |
| Source |
rdamedia |
| 338 ## - CARRIER TYPE |
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| Carrier type term |
online resource |
| Carrier type code |
cr |
| Source |
rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS |
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| File type |
text file |
| Encoding format |
PDF |
| Source |
rda |
| 490 1# - SERIES STATEMENT |
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| Series statement |
Springer Monographs in Mathematics, |
| International Standard Serial Number |
1439-7382 |
| 505 0# - FORMATTED CONTENTS NOTE |
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| Formatted contents note |
Unwinding proofs (‘Proof Mining’) -- Intuitionistic and classical arithmetic in all finite types -- Representation of Polish metric spaces -- Modified realizability -- Majorizability and the fan rule -- Semi-intuitionistic systems and monotone modified realizability -- Gödel’s functional (‘Dialectica’) interpretation -- Semi-intuitionistic systems and monotone functional interpretation -- Systems based on classical logic and functional interpretation -- Functional interpretation of full classical analysis -- A non-standard principle of uniform boundedness -- Elimination of monotone Skolem functions -- The Friedman A-translation -- Applications to analysis: general metatheorems I -- Case study I: Uniqueness proofs in approximation theory -- Applications to analysis: general metatheorems II -- Case study II: Applications to the fixed point theory of nonexpansive mappings -- Final comments. |
| 520 ## - SUMMARY, ETC. |
|---|
| Summary, etc. |
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. . |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Approximation theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Functional analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Operator theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematical logic. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Mathematical Logic and Foundations. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
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| Topical term or geographic name entry element |
Mathematics, general. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Approximations and Expansions. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Operator Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM |
|---|
| Topical term or geographic name entry element |
Functional Analysis. |
| 710 2# - ADDED ENTRY--CORPORATE NAME |
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| Corporate name or jurisdiction name as entry element |
SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY |
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| Title |
Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY |
|---|
| Relationship information |
Printed edition: |
| International Standard Book Number |
9783540775324 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE |
|---|
| Uniform title |
Springer Monographs in Mathematics, |
| International Standard Serial Number |
1439-7382 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS |
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| Uniform Resource Identifier |
http://dx.doi.org/10.1007/978-3-540-77533-1 |
| 912 ## - |
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| -- |
ZDB-2-SMA |
