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Graham R.L., Rothschild B.L., Spencer J.H. Ramsey Theory
Graham R.L., Rothschild B.L., Spencer J.H.  Ramsey Theory









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: Ramsey Theory

: Graham R.L., Rothschild B.L., Spencer J.H.

:

Ramsey theory has emerged as a cohesive subdiscipline of combinatorial analysis since about 1970. The present work comprises a self-contained exposition of the central results of Ramsey theory, describes recent developments in the field, and explores the influence of outside disciplines such as applications of topological dynamics and a combinatorial approach to undecidability results. New to the Second Edition is a complete treatment of Shelah's 1987 proof as well as the original proof of Van der Waerden's theorem.


: en

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ed2k: ed2k stats

: second edition

: 1990

: 196

: 11.01.2007

: | | ID
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(m,p,c-)-sets      7980
Abelian groups      80 88 123129
Ackermann function      61 171
Ackermann hierachy      6061 170171
Affine Ramsey theorem      42 68
Affine space      42
Ajtai, M.      109
Arithmetic progression      27 4546 97 155
arrow notation      1 7 119 169170 180
Artin, E.      30
Asymptotic values, graph Ramsey      101102
Asymptotic values, property B      104105
Asymptotic values, Ramsey      9296
Asymptotic values, van der Waerden      96 97 102103
Axiom of Choice      14 15 88 154 157 180
Baudets conjecture      29
Baumgartner, J.      84 88
Beck, J.      109
Behrend.F.A.      98 109
Bergelson, V.      165
Berlekamp, E.R.      109
Bipartite graphs      10 111 119
Bipartite Ramsey theorems      111114 119
Bolzano Weierstrass theorem      17
Boolean expressions      24
Bounded gaps      156 160
Bow tie      141
Bricks      135
Burkill, H.      17
Burling, J.P.      109
Burr, S.A.      140 147 150
Canonical coloring      129
Canonical Ramsey theorems      129
Canonical Ramsey theorems, bipartite      131
Canonical relations      23
Cantor Normal Form      171
Cates, M.L.      68
Chang, C.C      183
Choi, S.L.G.      109
Chromatic number      11 99 104
Chung, F.R.K.      143
Chvatal.V.      109 112 139 148
Columns condition      7374 124
Comfort.W.      169
Compactness principle, applications of      21 30 76 84 135 13".155 164 179
Compactness principle, proof of      1317 27
Concave functions      112
Conway, J.      61
cube      35 46 53
Cycles      143146
DeBruijn, N.G.      27
Density theorems      12 27 4546 99 111 143144
Deuber, W.      79 80 88 115 123
Difworth, R.P.      17
Dynamical system      155
Edge induced graph theorem      115
Enveloping semigroup      162
Epsilon-nought $(\varepsilon_0)$      171 173
Equations, nonhomogeneous regular      8788 136
Equations, over Abelian groups      80 123129
Equations, regular      9
Equations, regular homogeneous      71
Erdos cardinal      184
Erdos, P., conjectures of      54 119 146 148 151
Erdos, P., conjectures of, with E.Klein and G.Szekeres      25
Erdos, P., conjectures of, with L.Moser      18
Erdos, P., conjectures of, with P.Turan      13 4546
Erdos, P., conjectures of, with V.T.Sos      142
Erdos, P., influence of      26
Erdos, P., papers of      109 113 150
Erdos, P., papers of, with Burr      147
Erdos, P., papers of, with Burr, Spencer      140
Erdos, P., papers of, with Faudree, Rousseau, Schelp      149
Erdos, P., papers of, with Graham      141
Erdos, P., papers of, with Graham, Montgomery, Rothschild, Spencer, Straus      133
Erdos, P., papers of, with Hajnal      109 183
Erdos, P., papers of, with Hajnal, Rado      182
Erdos, P., papers of, with Lovasz      109
Erdos, P., papers of, with Moon      112
Erdos, P., papers of, with Rado      109 112 129
Erdos, P., papers of, with Spencer      109 112 113
Erdos, P., papers of, with Szekeres      17 2425
Ergodic theory      164
Euclidean plane      25 137
Euclidean Ramsey theorems      133
Euclidean space      4041 133
Existence argument      92 93 97 105 108 109
Exoo, G.      109
Faudree, R.      149 150
Fermats Last Theorem      69
Finite intersection property      157
Finite sums and products conjecture      84
Finite unions theorem      82
Fliptop      55
Folkman, J.      81 109 119
Folkmans theorem      81 88
Frankl, P.      109 123 137
Furstenberg, H.      46 53 153 165
Furstenbergs theorem      163 (see also Szemeredis theorem)
Gallais theorem      40 68 134
Game theory      4142
Giraud, G.      109
Glazer, S.      168
Gleason, A.M.      89 90 109
Godels Incompleteness Theorem      170
Gottschalk, W.H.      27
Graham Leeb Rothschild theorem      10 45 68
Graham, R.L.      68 109 112 123 133 141 143
Graham, R.L., conjecture of      66
Graph Ramsey theory      101 109 138151
Greenwood, R.E.      89 90 109
Grimstead, C      109
Grzegerczyk hierarchy      173
Guy, R.K.      112
Hajnal, A.      109 182 183
Hales Jewett theorem      10 3439 68
Hales Jewett theorem, and Moser conjecture      53
Hales Jewett theorem, applications of      43 83 119
Hales Jewett theorem, extended      40
Hales Jewett theorem, extended, and affine Ramsey theorem      44
Hales Jewett theorem, implications of      40
Hales Jewett theorem, Shelah proof      5460
Hales Jewett theorem, upper bounds      6068
Hales.A.W.      68
Harary, F.      139 148
Harrington, L.      170 180
Hilbert, D.      47
Hindman, N.      68 84 88 165 167
Hindmans theorem      84 88 133 168169
Hindmans theorem, topological      160
Homothety      40 134
Hypergraphs      11 99 104
Idempotent theorem      162 169
Inaccessible cardinals      184185
Induced coloring      6
Induced Ramsey theorems      114
Induced subgraphs      114
Infinite Ramsey theory      17 68 84 180
Infinite Ramsey theory, bipartite      114
Infinite Ramsey theory, canonical      129
Irving, R.      119 143
Isbell, J.R.      109
Jewett, R.I.      68
k-partite Ramsey theorem      112113
Kalbfleisch, J.G.      109
Katznelson, G.      53
Ketonen, J.      180
Keynes, J.M.      18
Klein, E.      25
Kleitman, D.J.      1
Kolmogoroff extension theorem      165
Komlos, J.      109
Kovari, T.      112
Kreisel, G.      180
Large disjoint collections      85
Large number      174
Large set (regular equations)      80
Large set (unprovable theorem)      169
Larson, J.      183
Lattice theory      10
Law of small numbers      90
Leeb, K.      68
Lovasz local lemma      9495 97 105 109
Lovasz, L.      94 109
Milliken, K.      88
Minimal property      156157
Mirsky, L.      17 88
Models      2425 66 180
Montgomery, P.      133
Moon, J.W.      112
Moore, G.E.      1819
Moser, L.      18 109
Moser, L., conjecture of      53 68
Motzkin, T.      27
Nesethl, J.      115 119 150
Ordinal numbers      171 182
Paris Harrington Theorem      170 180
Paris, J.      170 180
Partition regular      123125 129
Peano arithmetic      170 173 178
Pigeon Hole principle      7 30 39
Prime numbers      54
Principia Mathematica      18
Probabilistic method      92 148
Product topology      153 168
Promel, H.      123
Property B.      104106 109
Rado selection principle      27
Rado, R.      27 68 87 88
Rado, R. and I.Schur      71
Rado, R. and P.Erdos      109 112 129
Rado, R. and P.Erdos, A.Hajnal      182
Rado, R. and W.Deuber      80
Rados Theorem      10 71 74 104 124
Ramsey configurations      134
Ramsey functions      3 7 1617 22
Ramsey functions, asymptotics      see Asymptotic values
Ramsey functions, exact values      90 91
Ramsey functions, graphs      101102
Ramsey functions, Hales Jewett      6066
Ramsey functions, higher Ramsey numbers      106109
Ramsey functions, infinite      180
Ramsey functions, large      170
Ramsey functions, m(n)      105
Ramsey functions, ordinals      182183
Ramsey functions, Rado      104
Ramsey functions, Schur      103
Ramsey functions, van der Waerden      6268
Ramsey numbers      see Ramsey
Ramsey, F.P.      1825
Ramseys theorem, proof, abridged      35
Ramseys theorem, proof, unabridged      79 19 26
Ramseys theorem, proof, with ultrafilters      16
Random colorings      92 97
Ray Chaudhuri, D.K.      142
Restricted Ramsey theorems      119123
Reyner, S.W.      109
Roberts, S.      109
Rodl.V.      109 115 119 123 137 150
Rota, G.-C.      45
Roth, K.      13 46 68 98 109
Rothschild, B.L.      68 133
Roths theorem      46 68
Rousseau, C.C.      149
Russell, B.      18
Salem, R.      109
Sanders, J.      88
Schelp, R.      149 150
Schreier, O.      30
Schur numbers      see Ramsey functions
Schur, I.      29 6970 80 88
Schurs Theorem      9 69 88 103
Seidenberg, A.      27
Shelah proof      5460
Shelah, S.      54 57 68
Skolem, T.      26
smod p      73 74
Solovay, R.      180
Sos, V.T.      27 112 142
Spencer, D.C.      109
Spencer, J.H.      45 68 109 1 133 180
Sperners lemma      53
Spherical configurations      136
Stanton, R.      109
Stepping up lemma      106108
Straus, E.      27 88 133
Subadditive lemma      47
Sums      81
Symmetric hypergraph theorem      99
Szekeres, E.      2526
Szekeres, G.      17 2526
Szemeredi, E.      13 46 68 109
Szemeredis theorem      46 53 68
Szemeredis theorem, and Furstenbergs theorem      153 163165
Szemeredis theorem, application of      104
Tarsy, M.      26
Taylor, A.      133
Tic-Tac-Toe      41
Topological dynamics      153
Topological Hindman theorem      160
Topological van der Waerden theorem      155
Tournaments      18
Tower functions      61 106
Translations      137
Trees      137
Turan function      12
Turan, P.      2627 4546 112
Turans Theorem      13 145
Tychanoff theorem      15 153 164 168
Ultrafilters      166169
Van der Waerden, B.L.      29
van der Waerdens numbers      see Ramsey functions
van der Waerdens theorem      9 29 68
van der Waerdens theorem, and Hales Jewett theorem      3435 40
van der Waerdens theorem, and Szemeredis theorem      13
van der Waerdens theorem, applications of      76 78 81 83
van der Waerdens theorem, topological      153 155
Vector space Ramsey theorem      45 68
Vector spaces      10 4245
Veech, W.      165
Vertex-induced graph theorem      115
Wainer hierarchy      173
Walker, K      109
Weiss, B.      165
Whitehead, A.N.      18
Wilson, R.      142
Wittgenstein, L.      18
Wow function      61
Zarankiewiczs function      112
Znam, S.      112
Zorns Lemma      157 162 166
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