Ordered exponential fields:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2000]
|
| Series: | Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xviii, 166 Seiten |
| ISBN: | 0821809431 9780821809433 |
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MARC
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Record in the Search Index
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Contents
Introduction xiii
Chapter 0. Preliminaries on valued and ordered modules 1
1. Valued modules 1
2. Valuation independence 5
3. Ordered modules 7
Chapter 1. Non archimedean exponential fields 15
1. The natural valuation of an ordered field 15
2. The skeleton of (K 0, ,l, ) 18
3. Formally exponential fields 22
4. Lexicographic (de)composition of exponentials 24
5. Exponentiation in power series fields 27
6. Extensions and maximality 29
7. The structure theory for countable exponential fields 31
Chapter 2. Valuation theoretic interpretation of the growth and Taylor axioms 33
1. The axiom schemes (GA) and (T) 33
2. (GA) exponentials and the value group 34
3. Lifting exp from the residue field 36
4. (T) exponentials on the infinitesimals 37
5. Conclusion 39
6. Countable exponential fields with growth properties 40
7. Natural contractions arising from logarithms 44
Chapter 3. The exponential rank 49
1. Convex valuations 49
2. The exponential analogue of the rank 52
3. (GA) and (Ti) prelogarithms 53
4. The shift map Q 56
5. Characterization of the exponential and the principal exponential rank 61
Chapter 4. Construction of exponential fields 65
1. w Logarithmic cross sections 65
2. A combinatorial result and its consequences 67
3. Existence of logarithmic cross sections 70
4. From prelogarithms to logarithms 73
Chapter 5. Models for the elementary theory of the reals with restricted
analytic functions and exponentiation 77
1. Twisting a group cross section by an automorphism 77
xi
xii Contents
2. The exponential logarithmic power series field 79
3. Models of arbitrary principal exponential rank 83
Chapter 6. Exponential Hardy fields 89
1. Some basic valuation theory 89
2. Hardy fields 92
3. Value groups 97
4. The Hardy field of a polynomially bounded + (exp) expansion 98
5. Exponential boundedness 101
6. Levels 102
7. The Crucial Lemma for models of Tan 103
8. Residue fields of .F exp log closures 107
9. A truncation free solution to the Hardy problem 111
10. Undefinability of the Riemann ^ function 113
Appendix A. The model theory of contraction groups 117
1. Preliminaries 117
2. Cuts in ordered Abelian groups 118
3. Ordered abelian groups with contractions 120
4. Weak o minimality 136
Bibliography 155
Index 159
List of Notation 163 |
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| illustrated | Not Illustrated |
| indexdate | 2024-08-20T00:35:11Z |
| institution | BVB |
| isbn | 0821809431 9780821809433 |
| language | English |
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| physical | xviii, 166 Seiten |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs |
| series2 | Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs |
| spelling | Kuhlmann, Salma 1958- Verfasser (DE-588)114620020X aut Ordered exponential fields Salma Kuhlmann Providence, Rhode Island American Mathematical Society [2000] © 2000 xviii, 166 Seiten txt rdacontent n rdamedia nc rdacarrier Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs 12 Algèbre en théorie des modèles Corps ordonnés Model theoretic algebra Ordered fields Modelltheorie (DE-588)4114617-7 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Algebra (DE-588)4001156-2 s Modelltheorie (DE-588)4114617-7 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-3139-6 Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs 12 (DE-604)BV009737926 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008845024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kuhlmann, Salma 1958- Ordered exponential fields Fields Institute for Research in Mathematical Sciences <Toronto>: Fields Institute monographs Algèbre en théorie des modèles Corps ordonnés Model theoretic algebra Ordered fields Modelltheorie (DE-588)4114617-7 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4114617-7 (DE-588)4001156-2 |
| title | Ordered exponential fields |
| title_auth | Ordered exponential fields |
| title_exact_search | Ordered exponential fields |
| title_full | Ordered exponential fields Salma Kuhlmann |
| title_fullStr | Ordered exponential fields Salma Kuhlmann |
| title_full_unstemmed | Ordered exponential fields Salma Kuhlmann |
| title_short | Ordered exponential fields |
| title_sort | ordered exponential fields |
| topic | Algèbre en théorie des modèles Corps ordonnés Model theoretic algebra Ordered fields Modelltheorie (DE-588)4114617-7 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Algèbre en théorie des modèles Corps ordonnés Model theoretic algebra Ordered fields Modelltheorie Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008845024&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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