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Graham R.L., Rothschild B.L., Spencer J.H. — Ramsey Theory |
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Ïðåäìåòíûé óêàçàòåëü |
(m,p,c-)-sets 79—80
Abelian groups 80 88 123—129
Ackermann function 61 171
Ackermann hierachy 60—61 170—171
Affine Ramsey theorem 42 68
Affine space 42
Ajtai, M. 109
Arithmetic progression 27 45—46 97 155
arrow notation 1 7 119 169—170 180
Artin, E. 30
Asymptotic values, graph Ramsey 101—102
Asymptotic values, property B 104—105
Asymptotic values, Ramsey 92—96
Asymptotic values, van der Waerden 96 97 102—103
Axiom of Choice 14 15 88 154 157 180
Baudet’s 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 111—114 119
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 73—74 124
Comfort.W. 169
Compactness principle, applications of 21 30 76 84 135 13"’.155 164 179
Compactness principle, proof of 13—17 27
Concave functions 112
Conway, J. 61
cube 35 46 53
Cycles 143—146
DeBruijn, N.G. 27
Density theorems 12 27 45—46 99 111 143—144
Deuber, W. 79 80 88 115 123
Difworth, R.P. 17
Dynamical system 155
Edge induced graph theorem 115
Enveloping semigroup 162
Epsilon-nought 171 173
Equations, nonhomogeneous regular 87—88 136
Equations, over Abelian groups 80 123—129
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 45—46
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 24—25
Ergodic theory 164
Euclidean plane 25 137
Euclidean Ramsey theorems 133
Euclidean space 40—41 133
Existence argument 92 93 97 105 108 109
Exoo, G. 109
Faudree, R. 149 150
Fermat’s Last Theorem 69
Finite intersection property 157
Finite sums and products conjecture 84
Finite unions theorem 82
Fliptop 55
Folkman, J. 81 109 119
Folkman’s theorem 81 88
Frankl, P. 109 123 137
Furstenberg, H. 46 53 153 165
Furstenberg’s theorem 163 (see also “Szemeredi’s theorem”)
Gallai’s theorem 40 68 134
Game theory 41—42
Giraud, G. 109
Glazer, S. 168
Gleason, A.M. 89 90 109
Godel’s 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 101 109 138—151
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 34—39 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 54—60
Hales — Jewett theorem, upper bounds 60—68
Hales.A.W. 68
Harary, F. 139 148
Harrington, L. 170 180
Hilbert, D. 47
Hindman, N. 68 84 88 165 167
Hindman’s theorem 84 88 133 168—169
Hindman’s theorem, topological 160
Homothety 40 134
Hypergraphs 11 99 104
Idempotent theorem 162 169
Inaccessible cardinals 184—185
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 112—113
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 94—95 97 105 109
Lovasz, L. 94 109
Milliken, K. 88
Minimal property 156—157
Mirsky, L. 17 88
Models 24—25 66 180
Montgomery, P. 133
Moon, J.W. 112
Moore, G.E. 18—19
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 123—125 129
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. 104—106 109
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
Rado’s Theorem 10 71 74 104 124
Ramsey configurations 134
Ramsey functions 3 7 16—17 22
Ramsey functions, asymptotics see “Asymptotic values”
Ramsey functions, exact values 90 91
Ramsey functions, graphs 101—102
Ramsey functions, Hales — Jewett 60—66
Ramsey functions, higher Ramsey numbers 106—109
Ramsey functions, infinite 180
Ramsey functions, large 170
Ramsey functions, m(n) 105
Ramsey functions, ordinals 182—183
Ramsey functions, Rado 104
Ramsey functions, Schur 103
Ramsey functions, van der Waerden 62—68
Ramsey numbers see “Ramsey”
Ramsey, F.P. 18—25
Ramsey’s theorem, proof, abridged 3—5
Ramsey’s theorem, proof, unabridged 7—9 19 26
Ramsey’s theorem, proof, with ultrafilters 16
Random colorings 92 97
Ray — Chaudhuri, D.K. 142
Restricted Ramsey theorems 119—123
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
Roth’s 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 69—70 80 88
Schur’s Theorem 9 69 88 103
Seidenberg, A. 27
Shelah proof 54—60
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
Sperner’s lemma 53
Spherical configurations 136
Stanton, R. 109
Stepping up lemma 106—108
Straus, E. 27 88 133
Subadditive lemma 47
Sums 81
Symmetric hypergraph theorem 99
Szekeres, E. 25—26
Szekeres, G. 17 25—26
Szemeredi, E. 13 46 68 109
Szemeredi’s theorem 46 53 68
Szemeredi’s theorem, and Furstenberg’s theorem 153 163—165
Szemeredi’s 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. 26—27 45—46 112
Turan’s Theorem 13 145
Tychanoff theorem 15 153 164 168
Ultrafilters 166—169
Van der Waerden, B.L. 29
van der Waerden’s numbers see “Ramsey functions”
van der Waerden’s theorem 9 29 68
van der Waerden’s theorem, and Hales — Jewett theorem 34—35 40
van der Waerden’s theorem, and Szemeredi’s theorem 13
van der Waerden’s theorem, applications of 76 78 81 83
van der Waerden’s theorem, topological 153 155
Vector space Ramsey theorem 45 68
Vector spaces 10 42—45
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
Zarankiewicz’s function 112
Znam, S. 112
Zorn’s Lemma 157 162 166
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