An introduction to Ramsey theory: fast functions, infinity and metamathematics
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2018]
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| Schriftenreihe: | Student mathematical library
volume 87 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xiv, 207 Seiten Illustrationen |
| ISBN: | 9781470442903 |
Internformat
MARC
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| 245 | 1 | 0 | |a An introduction to Ramsey theory |b fast functions, infinity and metamathematics |c Matthew Katz, Jan Reimann |
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| 264 | 4 | |c © 2018 | |
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Datensatz im Suchindex
| _version_ | 1804179267642195968 |
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| adam_text | Contents Foreword: MASS at Penn State University vii Preface ix Chapter 1. Graph Ramsey theory 1 §1.1. The basic setting 1 §1.2. The basics of graph theory 4 §1.3. Ramsey’s theorem for graphs 14 §1.4. Ramsey numbers and the probabilisticmethod 21 §1.5. Turán’s theorem 31 §1.6. The finite Ramsey theorem 34 Chapter 2. Infinite Ramsey theory 41 §2.1. The infinite Ramsey theorem 41 §2.2. König’s lemma and compactness 43 §2.3. Some topology 50 §2.4. Ordinals, well-orderings, and the axiomof choice 55 §2.5. Cardinality and cardinal numbers 64 §2.6. Ramsey theorems for uncountable cardinals 70 §2.7. Large cardinals and Ramsey cardinals 80 v
Contents VI Chapter 3. Growth ofRamsey functions 85 §3.1. Van der Waerden’s theorem 85 §3.2. Growth of van der Waerden bounds 98 §3.3. Hierarchies of growth 105 §3.4. The Hales-Jewett theorem 113 §3.5. A really fast-growing Ramsey function 123 Chapter 4. Metamathematics 129 §4.1. Proof and truth 129 §4.2. Non-standard models of Peano arithmetic 145 §4.3. Ramsey theory in Peano arithmetic 152 §4.4. Incompleteness 159 §4.5. Indiscernibles 171 §4.6. Diagonal indiscernibles via Ramsey theory 182 §4.7. The Paris-Harrington theorem 188 §4.8. More incompleteness 193 Bibliography 199 Notation 203 Index 205
This book takes the reader on a journey through Ramsey theory, from graph theory and combinatorics to set theory to logic and metamath ematics. Written in an informal style with few requisites, it develops two basic principles of Ramsey theory: many combinatorial properties persist under partitions, but to witness this persistence, one has to start with very large objects. The interplay between those two principles not only produces beautiful theorems but also touches the very foundations of mathematics. In the course of this book, the reader will learn about both aspects. Among the topics explored are Ramsey’s theorem for graphs and hypergraphs, van der Waerden’s theorem on arithmetic progressions, infi nite ordinals and cardinals, fast growing functions, logic and provability, Gödel incompleteness, and the Paris-Harrington theorem. Quoting from the book, “There seems to be a murky abyss lurking at the bottom of mathematics. While in many ways we cannot hope to reach solid ground, mathematicians have built impressive ladders that let us explore the depths of this abyss and marvel at the limits and at the power of mathematical reasoning at the same time. Ramsey theory is one of those ladders.”
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| any_adam_object | 1 |
| author | Katz, Matthew 1986- Reimann, Jan 1971- |
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| ctrlnum | (OCoLC)1077761373 (DE-599)BSZ513702954 |
| discipline | Mathematik Philosophie |
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| id | DE-604.BV045399918 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:17:09Z |
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| isbn | 9781470442903 |
| language | English |
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| physical | xiv, 207 Seiten Illustrationen |
| publishDate | 2018 |
| publishDateSearch | 2018 |
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| publisher | American Mathematical Society |
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| series | Student mathematical library |
| series2 | Student mathematical library |
| spelling | Katz, Matthew 1986- Verfasser (DE-588)1171436998 aut An introduction to Ramsey theory fast functions, infinity and metamathematics Matthew Katz, Jan Reimann Providence, Rhode Island American Mathematical Society [2018] © 2018 xiv, 207 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Student mathematical library volume 87 Ramsey-Theorie (DE-588)4212682-4 gnd rswk-swf Ramsey-Theorie (DE-588)4212682-4 s DE-604 Reimann, Jan 1971- Verfasser (DE-588)1171437447 aut Erscheint auch als Online-Ausgabe 978-1-4704-4994-0 Student mathematical library volume 87 (DE-604)BV013184751 87 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030786036&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030786036&sequence=000003&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Katz, Matthew 1986- Reimann, Jan 1971- An introduction to Ramsey theory fast functions, infinity and metamathematics Student mathematical library Ramsey-Theorie (DE-588)4212682-4 gnd |
| subject_GND | (DE-588)4212682-4 |
| title | An introduction to Ramsey theory fast functions, infinity and metamathematics |
| title_auth | An introduction to Ramsey theory fast functions, infinity and metamathematics |
| title_exact_search | An introduction to Ramsey theory fast functions, infinity and metamathematics |
| title_full | An introduction to Ramsey theory fast functions, infinity and metamathematics Matthew Katz, Jan Reimann |
| title_fullStr | An introduction to Ramsey theory fast functions, infinity and metamathematics Matthew Katz, Jan Reimann |
| title_full_unstemmed | An introduction to Ramsey theory fast functions, infinity and metamathematics Matthew Katz, Jan Reimann |
| title_short | An introduction to Ramsey theory |
| title_sort | an introduction to ramsey theory fast functions infinity and metamathematics |
| title_sub | fast functions, infinity and metamathematics |
| topic | Ramsey-Theorie (DE-588)4212682-4 gnd |
| topic_facet | Ramsey-Theorie |
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