000 02556cam a2200277 i 4500
001 137675
003 ISI Library, Kolkata
005 20170517114311.0
008 160113s2016 riu b 001 0 eng
020 _a9781470428082
040 _aISI Library
082 0 0 _a510MS
_223
_bAm512
100 1 _aDodos, Pandelis,
_eauthor
245 1 0 _aRamsey theory for product spaces /
_cPandelis Dodos and Vassilis Kanellopoulos.
260 _aProvidence :
_bAmerican Mathematical Society,
_c©2016.
300 _aix, 245 pages ;
_c26 cm.
490 0 _aMathematical surveys and monographs ;
_vv 212.
504 _aIncludes bibliographical references and index.
505 0 _aChapter 1. Basic concepts -- Part 1. Coloring theory -- Chapter 2. Combinatorial spaces -- Chapter 3. Strong subtrees -- Chapter 4. Variable words -- Chapter 5. Finite sets of words -- Part 2. Density theory -- Chapter 6. Szemerédi's regularity method -- Chapter 7. The removal lemma 120 -- Chapter 8. The density Hales-Jewett theorem -- Chapter 9. The density Carlson-Simpson theorem -- Part 3. Appendices -- Appendix A. Primitive recursive functions -- Appendix B. Ramsey's theorem -- Appendix C. The Baire property -- Appendix D. Ultrafilters -- Appendix E. Probabilistic background -- Appendix F. Open problems.
520 _aRamsey theory is a dynamic area of combinatorics that has various applications in analysis, ergodic theory, logic, number theory, probability theory, theoretical computer science, and topological dynamics. This book is devoted to one of the most important areas of Ramsey theory--the Ramsey theory of product spaces. It is a culmination of a series of recent breakthroughs by the two authors and their students who were able to lift this theory to the infinite-dimensional case. The book presents many major results and methods in the area, such as Szemerédi's regularity method, the hypergraph removal lemma, and the density Hales-Jewett theorem. This book addresses researchers in combinatorics but also working mathematicians and advanced graduate students who are interested in Ramsey theory. The prerequisites for reading this book are rather minimal: it only requires familiarity, at the graduate level, with probability theory and real analysis. Some familiarity with the basics of Ramsey theory would be beneficial, though not necessary.
650 0 _aRamsey theory.
650 0 _aCombinatorial analysis.
650 0 _aTopological spaces.
700 1 _aKanellopoulos, Vassilis,
_eauthor
942 _2ddc
_cBK
999 _c423573
_d423573