Monk J.D. (ed.) — Handbook of Boolean Algebras, Vol. 1 :: Электронная библиотека попечительского совета мехмата МГУ

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Monk J.D. (ed.) — Handbook of Boolean Algebras, Vol. 1

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Название: Handbook of Boolean Algebras, Vol. 1

Автор: Monk J.D. (ed.)

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: second

Год издания: 1989

Количество страниц: 344

Добавлена в каталог: 09.06.2009

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Предметный указатель

Quasi-partition      227
Quotient algebra      47ff 49 65 75ff 247 266
Quotient modulo a filter, an ideal      75ff
Quotient space      107
Quotient structure      301
Rabin, M.      298 302 310
Rank function      283
Rasiowa — Sikorski lemma      5 35ff
Rasiowa, H.      3 35 310
Realization of a set of formulas      292
Reduced representation      101 111
Refinement property      216
Regular $\omega_{1}$ -Aronszajn tree      231
Regular closed      28
Regular open algebra      5 7 25 42 60 102 172f 182 228ff 236
Regular open algebras of trees      173 228ff
Regular open set      25
Regular subalgebra      21 59 163
Regular tree      231
Regularization of a      25
Relative algebra      5 7 38ff 63 88 105 179
Relatively complete subalgebra      123 163 300ff
Relevant points of a      249
Representability      173 212 236f
Representation of a BA      101
retract      71
Retraction      71
Retractive BA      239 241 250
Rigid BA      239 263
Rigid tree algebra      255
RO(X)      25 28f 37 42 56 58 64 102f 172 175 183 191f 214 221ff 270
Roitman, J.      154 271 283
Root of a tree      226 255
Rubin's theorem on chains and antichains      253
Rubin's theorem on retractive BAs      250
Rubin's undecidability theorem      302
Rubin, J.E.      33 310
Rubin, M.      241 248 254 263 287 299 302 309
Rudin — Keisler order      208
Ryll-Nardzewski, C.      33 310
sat (A)      41 43
Satisfies Baire's theorem      182
Saturation      38 41
Scattered space      271
Schlechta, K.      2
Schlingmann, D.      2
Schroeder — Bernstein property      173 179f
Schwartz, J.T.      23 309
Scott's Theorem      74
Scott, D.      4 33 310
Second normal form lemma for elements in a tree algebra      258
Section of a sheaf      117f
Semantic embedding      285 301
Separates points      106
Separative partial order      58 65 226
Shapirovskii's theorems on independence      139f
Shapirovskii, B.      141 153 166 206 284
Sheaf      140 153 287
Sheaf associated with $A\subseteq B$       121 153
Sheaf of BAs      119ff
Sheaf of L-structures      120
Sheaf of sets      117
Sheaf representation      93 107 116
Sheaf space      117
Sheaf theory      163
Sheffer stroke      27
Sheffer, H.      3 310
Shelah's theorem on independence      139 140 145
Shelah's theorem on pairwise incomparable families      62
Shelah's theorem on the number of ideals      145
Shelah, S.      2 50 62 140 144f 252 310
Sikorksi's extension criterion      65 67 131 160 170 242 257
Sikorksi's extension theorem      47 70 154 208 250
Sikorksi, R.      3 35 88 176 189 213
Simon, P.      2
Simple extension of a BA      53 69 85 123 125
Solovay's theorem      225
Solovay, R.M.      4 37 190f 231 310
Souslin algebra      175 190 212 236
Souslin continuum      236
Souslin lines      175
Souslin tree      212 228ff 252
Space of orderings of a field      106
Space of ultrafilters      99
Special Classes of Boolean Algebras, $(-\infty, a]$ , $\{x:x\leq a\}$       242
Special Classes of Boolean Algebras, $(a, +\infty)$ , {x:a<x}      242
Special Classes of Boolean Algebras, $(c_{\alpha})_{a\leq\alpha(A)}$ , cardinal sequence of A      278
Special Classes of Boolean Algebras, $A_{\alpha}$ , $\alpha$ th Cantor — Bendixson derivative of X      274
Special Classes of Boolean Algebras, $A_{\rho k}$ , Intalg( $\omega^{\rho}\cdot\kappa$ )      273
Special Classes of Boolean Algebras, $b_{t}$ , $\{s\in T:t\leq s\}$ (for a tree T)      255
Special Classes of Boolean Algebras, $B_{T}$ , tree algebra over T      255
Special Classes of Boolean Algebras, $I_{\alpha}$ , $\alpha$ th Cantor — Bendixson ideal      273
Special Classes of Boolean Algebras, $I_{\infty}$ , union of all $I_{\alpha}$ 's      273
Special Classes of Boolean Algebras, $M\ll N$ , $\forall m\in M\forall n\in N(m<n)$       242
Special Classes of Boolean Algebras, $T\lceil t$ , subtree $\{s\in T:t\leq s\}$ of $T^{n}$       260
Special Classes of Boolean Algebras, $T_{\alpha\lambda}$ , set of sequences of members of $\alpha$ of length $<\lambda$       262
Special Classes of Boolean Algebras, $x<\cdot y$ , x immediately <y      243
Special Classes of Boolean Algebras, $\alpha(A)$ , first Cantor — Bendixson invariant of A      275
Special Classes of Boolean Algebras, I(A), ideal generated by the atoms      273
Special Classes of Boolean Algebras, Int(a), set of intervals constituting a      249
Special Classes of Boolean Algebras, Is(X), set of isolated points of X      274
Special Classes of Boolean Algebras, l(a), length of an element a in an interval algebra      249
Special Classes of Boolean Algebras, n(A), second Cantor — Bendixson invariant of A      275

Special Classes of Boolean Algebras, rel(a), set of relevant points of a      249
Special Classes of Boolean Algebras, succ(x), set of immediate successors of x      261
Special Classes of Boolean Algebras, X', set of non-isolated points of X      274
SPREAD      145 157
Stalk of a sheaf      117
Standard representation of an element in an interval algebra      242
Stationary set      140 143 147
Stavi, J.      192
Stepanek, P.      2
Stone duality      3 129 157
Stone map      33 99ff
Stone monomorphism      101
Stone space      99ff 114ff 132 177 245
Stone topology      99
Stone — Cech compactification      95 111 113ff
Stone — Cech remainder      95
Stone's theorem      3 5 7 9 20ff 28 34 49 59 78 92f 99 176 181
Stone, M.H.      3 310
Strictly positive measure      46 233
Strictly smaller      28
Strong countable separation property      81 85
Subalgebra generated by X      51
Subalgebra of a BA      10 47ff 93 109
Subtree      260
Successor of an element of a tree      261
Sum of elements      8 20
Superatomic BA      138 154 157 166 239 241 271ff
Symmetric difference      18
Taiclin, M.A.      302 309
Taimanov, A.D.      302 309
Tarski's cube problem      85 89 91
Tarski's decidability theorem      287
Tarski's Schroeder — Bernstein theorem      180
Tarski, A.      88 180 187 197
Theory      11 287
Thin-tall space      271
Three-parameter distributivity      173 212 223
Todorcevic, S.      2 144 158 310
Topological counterparts      96
Topological duality      93 see
Topological Duality, $f^{d}$ , dual of the homomorphism f      107
Topological Duality, $pr_{A}(b)$ , $max\{a\in A:a\leq b\}$ , given $A\subseteq B$       123
Topological Duality, $\alpha X$ , one-point compactification of X      115
Topological Duality, $\bar{p}$ , filter generated by p in B, p a filter on $&#192;\subseteq &#194;$       120
Topological Duality, $\beta X$ , Stone — Cech compactification of X      114
Topological Duality, $\Gamma(\mathscr{S})$ , $\Gamma_{X}(\mathscr{S})$ , set of global sections      117
Topological Duality, $\Gamma_{u}(\mathscr{S})$ , set of local sections of $\mathscr{S}$ over u      117
Topological Duality, $\phi^{d}$ , dual of the continuous map $\phi$       107
Topological Duality, $\pi_{p}$ , canonical quotient mapping for p      120
Topological Duality, $\|f = g\|$ , $\{p\in u: f(p) = g(p)\}$ , in a sheaf      117
Topological Duality, 2, 2, with the discrete topology      100
Topological Duality, t(x), $\{a\in Clop X:x\in a\}$       100
Totally disconnected space      97
TREE      225 254ff
Tree algebras      239ff 254ff
Tree algebras and interval algebras      267ff
Treybig — Ward theorem      246ff
Treybig, L.      248 310
Trivial BA      9
Trivial filter      31
Trivial ideal      76
Truth-table method      35
Truth-value in a BA      193
Two-element BA      9 34
Tychonoff space      112 114
Tychonoff's theorem      33
Ult A      31 33f 37 82ff 95ff 157 163 172
Ultrafilter      32ff 95ff 262
Ultrafilters in a tree algebra      262
Ultraproduct      92
Undecidability      285 299ff
Uniqueness of amalgamated free products      168
Uniqueness of complements      16
Uniqueness of free BAs      130
Uniqueness of free products      158
Uniqueness of the completion of a BA      60
Uniqueness of the completion of a partial order      56
Universal algebra      129
Universal property of products      87
Upper bound      14
Upper projection      142
Urysohn's theorem      104
Van Douwen, E.K.      263 267 309
Variety      49
Vaught relation      72 90 288 293
Vaught's isomorphism theorem      47 65 72 84 90 96 276f
Vaught, R.L.      72 90
Vladimirov's lemma      201
Vladimirov, D.      201 203f
Vojtas, P.      44ff
von Neumann, J.      182
Vopenka, P.      4
Walker, R.C.      177 310
Ward, A.J.      248
Weak distributivity      173 212 232ff
Weak product of BAs      87 107 112 138 254
Weakly compact cardinal      144
Weakly homogeneous BAs      255 270
Weakly inaccessible cardinal      41 166
Weese, M.      2 107 287 300
Weight of a space      104
Weiss, W.      271 310
Zero-dimensional space      96
Zorn's lemma      33 40 55 61 70 151 201 250

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