Asymptotic differential algebra and model theory of transseries / (Record no. 81375)
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| 001 - CONTROL NUMBER | |
| control field | ocn986538411 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | OCoLC |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20220908100126.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu---unuuu |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 170510s2017 nju ob 001 0 eng d |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | N$T |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | N$T |
| Modifying agency | JSTOR |
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| -- | OCLCO |
| 019 ## - | |
| -- | 984643717 |
| -- | 992529801 |
| -- | 1175644013 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781400885411 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 1400885418 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780691175423 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 069117542X |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780691175430 |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 0691175438 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1515/9781400885411 |
| Source of number or code | doi |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000060745788 |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000067041914 |
| 029 1# - OTHER SYSTEM CONTROL NUMBER (OCLC) | |
| OCLC library identifier | AU@ |
| System control number | 000069876134 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)986538411 |
| Canceled/invalid control number | (OCoLC)984643717 |
| -- | (OCoLC)992529801 |
| -- | (OCoLC)1175644013 |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 22573/ctt1hsw1jw |
| Source of stock number/acquisition | JSTOR |
| 037 ## - SOURCE OF ACQUISITION | |
| Stock number | 9452657 |
| Source of stock number/acquisition | IEEE |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA295 |
| Item number | .A87 2017eb |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT |
| Subject category code subdivision | 002040 |
| Source | bisacsh |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT002010 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512/.56 |
| Edition number | 23 |
| 049 ## - LOCAL HOLDINGS (OCLC) | |
| Holding library | MAIN |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Aschenbrenner, Matthias, |
| Dates associated with a name | 1972- |
| 9 (RLIN) | 64940 |
| 245 10 - TITLE STATEMENT | |
| Title | Asymptotic differential algebra and model theory of transseries / |
| Statement of responsibility, etc. | Matthias Aschenbrenner, Lou van den Dries, Joris van der Hoeven. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Princeton : |
| Name of producer, publisher, distributor, manufacturer | Princeton University Press, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2017. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| File type | text file |
| 347 ## - DIGITAL FILE CHARACTERISTICS | |
| Encoding format | |
| 490 1# - SERIES STATEMENT | |
| Series statement | Annals of mathematics studies ; |
| Volume/sequential designation | number 195 |
| 504 ## - BIBLIOGRAPHY, ETC. NOTE | |
| Bibliography, etc. note | Includes bibliographical references and index. |
| 588 0# - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Print version record. |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover; Title; Copyright; Contents; Preface; Conventions and Notations; Leitfaden; Dramatis Person�; Introduction and Overview; A Differential Field with No Escape; Strategy and Main Results; Organization; The Next Volume; Future Challenges; A Historical Note on Transseries; 1 Some Commutative Algebra; 1.1 The Zariski Topology and Noetherianity; 1.2 Rings and Modules of Finite Length; 1.3 Integral Extensions and Integrally Closed Domains; 1.4 Local Rings; 1.5 Krull's Principal Ideal Theorem; 1.6 Regular Local Rings; 1.7 Modules and Derivations; 1.8 Differentials. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 1.9 Derivations on Field Extensions2 Valued Abelian Groups; 2.1 Ordered Sets; 2.2 Valued Abelian Groups; 2.3 Valued Vector Spaces; 2.4 Ordered Abelian Groups; 3 Valued Fields; 3.1 Valuations on Fields; 3.2 Pseudoconvergence in Valued Fields; 3.3 Henselian Valued Fields; 3.4 Decomposing Valuations; 3.5 Valued Ordered Fields; 3.6 Some Model Theory of Valued Fields; 3.7 The Newton Tree of a Polynomial over a Valued Field; 4 Differential Polynomials; 4.1 Differential Fields and Differential Polynomials; 4.2 Decompositions of Differential Polynomials; 4.3 Operations on Differential Polynomials. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 4.4 Valued Differential Fields and Continuity4.5 The Gaussian Valuation; 4.6 Differential Rings; 4.7 Differentially Closed Fields; 5 Linear Differential Polynomials; 5.1 Linear Differential Operators; 5.2 Second-Order Linear Differential Operators; 5.3 Diagonalization of Matrices; 5.4 Systems of Linear Differential Equations; 5.5 Differential Modules; 5.6 Linear Differential Operators in the Presence of a Valuation; 5.7 Compositional Conjugation; 5.8 The Riccati Transform; 5.9 Johnson's Theorem; 6 Valued Differential Fields; 6.1 Asymptotic Behavior of vP; 6.2 Algebraic Extensions. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 6.3 Residue Extensions6.4 The Valuation Induced on the Value Group; 6.5 Asymptotic Couples; 6.6 Dominant Part; 6.7 The Equalizer Theorem; 6.8 Evaluation at Pseudocauchy Sequences; 6.9 Constructing Canonical Immediate Extensions; 7 Differential-Henselian Fields; 7.1 Preliminaries on Differential-Henselianity; 7.2 Maximality and Differential-Henselianity; 7.3 Differential-Hensel Configurations; 7.4 Maximal Immediate Extensions in the Monotone Case; 7.5 The Case of Few Constants; 7.6 Differential-Henselianity in Several Variables; 8 Differential-Henselian Fields with Many Constants. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 8.1 Angular Components8.2 Equivalence over Substructures; 8.3 Relative Quantifier Elimination; 8.4 A Model Companion; 9 Asymptotic Fields and Asymptotic Couples; 9.1 Asymptotic Fields and Their Asymptotic Couples; 9.2 H-Asymptotic Couples; 9.3 Application to Differential Polynomials; 9.4 Basic Facts about Asymptotic Fields; 9.5 Algebraic Extensions of Asymptotic Fields; 9.6 Immediate Extensions of Asymptotic Fields; 9.7 Differential Polynomials of Order One; 9.8 Extending H-Asymptotic Couples; 9.9 Closed H-Asymptotic Couples; 10 H-Fields; 10.1 Pre-Differential-Valued Fields. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems. This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences. |
| 546 ## - LANGUAGE NOTE | |
| Language note | In English. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | IEEE |
| Provenance (VM) [OBSOLETE] | IEEE Xplore Princeton University Press eBooks Library |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Series, Arithmetic. |
| 9 (RLIN) | 64941 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Divergent series. |
| 9 (RLIN) | 64942 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Asymptotic expansions. |
| 9 (RLIN) | 64943 |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Differential algebra. |
| 9 (RLIN) | 64944 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | S�eries arithm�etiques. |
| 9 (RLIN) | 64945 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | S�eries divergentes. |
| 9 (RLIN) | 64946 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | D�eveloppements asymptotiques. |
| 9 (RLIN) | 64947 |
| 650 #6 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Alg�ebre diff�erentielle. |
| 9 (RLIN) | 64948 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | arithmetic progressions. |
| Source of heading or term | aat |
| 9 (RLIN) | 64949 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | MATHEMATICS |
| General subdivision | Algebra |
| -- | Intermediate. |
| Source of heading or term | bisacsh |
| 9 (RLIN) | 64159 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | MATHEMATICS |
| General subdivision | Algebra |
| -- | Abstract. |
| Source of heading or term | bisacsh |
| 9 (RLIN) | 64950 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Asymptotic expansions. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst00819868 |
| 9 (RLIN) | 64943 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Differential algebra. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst00893436 |
| 9 (RLIN) | 64944 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Divergent series. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst00895691 |
| 9 (RLIN) | 64942 |
| 650 #7 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Series, Arithmetic. |
| Source of heading or term | fast |
| Authority record control number or standard number | (OCoLC)fst01113175 |
| 9 (RLIN) | 64941 |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 9 (RLIN) | 3294 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Van den Dries, Lou. |
| 9 (RLIN) | 64951 |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Hoeven, J. van der |
| Fuller form of name | (Joris) |
| 9 (RLIN) | 64952 |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Aschenbrenner, Matthias, 1972- |
| Title | Asymptotic differential algebra and model theory of transseries |
| International Standard Book Number | 9780691175423 |
| Record control number | (DLC) 2017005899 |
| -- | (OCoLC)962354550 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Annals of mathematics studies ; |
| Volume/sequential designation | no. 195. |
| 9 (RLIN) | 64953 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ieeexplore.ieee.org/servlet/opac?bknumber=9452657">https://ieeexplore.ieee.org/servlet/opac?bknumber=9452657</a> |
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