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

Ershov — Rabin method      302
Ershov, Y.      302 309
Existence of amalgamated free products      168
Existence of completion of a BA      60
Existence of completion of a partial order      56
Existence of free BA      131
Existence of free products      158
Extension to homomorphisms      67ff 164 242f 257f
Extremally disconnected space      103 125 207
F-space      177 208
Factor algebra      39 180
Feferman, S.      33 309
Fichtenholz — Kantorovich — Hausdorff example      138
Fichtenholz, G.      129 138
Filter dual to an ideal      75
Filter generated by E in A      32
Filter in a BA      31
Filters and closed sets      105
Finite BA      8 30 53 84 102 132 272
Finite extensions of a BA      53
Finite graph      302
Finite intersection property      32ff
Finite-cofinite BA      10 103 254 272
Finitely additive measure      46 85 139
Finitely distinguished      197
Finitely satisfiable set of formulas      294
First category      182
First normal form lemma for elements in a tree algebra      256
Fodor's Theorem      140 143
Forcing      27 41 50 58 190
Fr(A)      206
Franek, F.      139
Free $\kappa$ -complete BA      184 189
Free $\sigma$ -complete BA      184
Free BA      127 129ff 161 175 211 241 247
Free complete BA      191
Free constructions      127
Free Constructions, $<X>^{cm}$ , complete subalgebra generated by X      141
Free Constructions, $<X>^{\kappa-cm}$ , $\kappa$ -subalgebra generated by X      141
Free Constructions, $A_{1}\oplus\cdots\oplus A_{n}$ , free product of $A_{1},\ldots, A_{n}$       161
Free Constructions, $Fr \kappa$ , free BA on $\kappa$ free generators      132
Free Constructions, $\oplus_{i\in I}A_{i}$ , free product of the $A_{i}$ 's      161
Free Constructions, $\pi\chi A$ , pseudo-character of A      153
Free Constructions, $\pi\chi_{A}(q)$ , pseudo-character of the filter q      153
Free Constructions, $\stackrel{\oplus}{C^{i\in I}}A_{i}$ , amalgamated free product      171
Free Constructions, Id(B), set of ideals of B      150
Free Constructions, ind B, independence of B      137
Free Constructions, ind*A, (related to independence)      153
Free Constructions, lpr(x, C), lower projection of x w.r.t. C      142 146
Free Constructions, s*X, sup{ $|Y|^{+}$ : Y is a discrete subspace of X}      145
Free Constructions, sX, spread of X      145
Free Constructions, upr(x, C), upper projection of x w.r.t. C      142 146
Free products of BAs      127ff 157ff 175
Freely generated      131
Fremlin, D.H.      2
Frolik's theorem      173 207ff
Frolik, Z.      190 207 309
Functional analysis      20
Gaifman — Hales theorem      190 212
Gaifman, H.      141 191
Galvin, F.      158 309
Generation of ultrafilters      45
Generators      51
Generic filters      35
Gleason spaces      125
Global sections of a sheaf      117
Goernemann, B.      2
Graetzer, G.      164
Graph (finite)      302
Greatest element      14
Greatest lower bound      14
Hajnal, A.      145
Hales, A.      141 191
Half-open interval      10
Halmos, P.R.      91 309
Halpern, J.D.      33 309
Hanf's example      47 88 176
Hanf, W.      86 89 91 309
Hausdorff sheaf      117
Hausdorff, F.      129 138 see
Height (of an element in a tree)      226
Height of a tree      226
Hereditarily disconnected space      97
Hodel, R.      145 309
Homogeneous (w.r.t. a function)      198
Homogeneous BA      127 135 164ff 181 188 192 255
Homogeneous partial order      181
Homogeneous space      139 208
Homogeneous tree algebra      270
Homomorphic extension      47
Homomorphic images      49
Homomorphism      8 47 65 77 93 106ff
Homomorphism of squares      185
Homomorphism theorem      77
Huntington, E.      3 309
Ideal dual to a filter      75
Ideal generated by E      76
Ideal of measure zero sets      75
Ideal-independent subset      145 148
Ideals      47 65 74ff 85 105 145ff
Ideals and open sets      105
Idempotence law      13
Idempotent      19 20
Immediate successor (in a tree)      261
Incomparable elements      47 62
Incompatible elements of a partial order      55
Ind A      199 137ff
Independence      127 137ff 166 172 190 196ff 249
Independent family of subalgebras      159 200 249
Independent part of an element      125
Independent set of partitions      199ff
Independent subalgebras      162
Independent subset of a BA      131
Independent subset, size of      136
Independently generated Boolean algebra      131
Inequalities in BAs      34
Infinite distributive laws      175 182
Infinite operation      5 20 173
Infinite Operations, $F_{\sigma}$ -set, usual topological notion      176
Infinite Operations, $L_{\infty\omega}$ , usual infinitary logic      193
Infinite Operations, $L_{\kappa\omega}$ , usual infinitary logic      193
Infinite Operations, $U_{\alpha}$ , set of elements of level $\alpha$       226
Infinite Operations, $\mathbf{C}_{csp}$ , class of BAs with countable separation property      176
Infinite Operations, $\mathbf{C}_{\infty}$ , class of complete BAs      175
Infinite Operations, $\mathbf{C}_{\kappa}$ , class of $\kappa$ -complete BAs      175
Infinite Operations, $\mathbf{C}_{\sigma}$ , class of $\sigma$ -complete BAs      175
Infinite Operations, $\pi(A)$ , density of A      199
Infinite Operations, $\tau(A)$ , complete generation of A      199 204
Infinite Operations, c(A), cellularity of A      199
Infinite Operations, card(A), cardinality of A      199
Infinite Operations, height(T), height of T      226
Infinite Operations, pred(t), set of predecessors of t      225
Infinite Operations, T*, opposite ordering to T      226
Infinite product      20
Infinite sum      20
Initial chain in a tree algebra      270
Initial chain of a tree      262
Initial segment of a linear order      244
Injective      173 186
IntalgL      10f 241ff 270ff
Interior      25
Intermediate algebra      113
Interval algebra      10 22 46 91 138 239 241 255 272 290
Irreducible map      125
Irredundance      47 61
Isolated points      103
Isomorphism of BAs      16
Isomorphism of commutative squares      185
Jech, T.      213 228 231 310
Jensen, R.B.      231

Johnsbraten, H.      231 309
Join      8
Juhasz, I.      145f 271 310
Jump in a linear ordering      243
Kantorovich, L.      129 138 see
Kaplansky, I.      89 310
Karp's example      221
Karp, C.      221
Keisler, H.J.      287 309
Kelley, J.L.      33 310
Kernel of a homomorphism      76
Ketonen, J.      72 91 310
Koppelberg's theorem      177
Koppelberg, B.      2
Koppelberg, S.      1 5 47 72 93 124 127 173 177 239 285 311
Kripke's embedding theorem      192 223 227
Kripke, S.      190 192
Kunen, K.      50 158 310
L-theory      287
LaGrange's theorem on amalgamated free products      186
LaGrange's theorem on cardinal sequences      278ff
Lagrange, R.      186 271f 283
Lattice      5 7 14 15
Lattice of ideals of a BA      84
Lattice of subalgebras      254
Lavrov, I.      302 309
Least element      14
Least upper bound      14
Lebesgue measure      21 234 237
Lebesgue, H.      234
Length of an element of an interval algebra      249
Level in a tree      226
Levy, A.      33 309
Lindenbaum — Tarski algebra      5 7 11 12 37 139 299 see
Local sections of a sheaf      117
Locally compact space      115
Loomis — Sikorski theorem      173 176 181ff 221ff
Los, J.      33 310
Lower bound      14
Lower projection      142
Maharam's theorem      234
Maharam, D.      2 182 234 310
Martin's Axiom      37 41 46 65 158 228 231 252
Martin, D.A.      37 310
Maximal filter      32
Maximally disjoint (ideal and subalgebra)      250
Maximally irredundant set      61 62
McAloon's theorem      227 231
McAloon, K.      226 227
McKenzie's proof for Rubin's undecidability theorem      302ff
McKenzie's proposition on irredundance      62
McKenzie's theorem on complete generation      205
McKenzie, R.      50 62 190 199 205 287 300 302f 309
Meager      21 28 182
Meager Borel sets      76
Measure algebra      233ff
Meet      8
Metamathematics, $E_{i}$ , ideals formed by iterating E(A)      288
Metamathematics, $L_{M}$ , language obtained by adding constants for elements of M      294
Metamathematics, $L_{U}$ , language for Boolean pairs      300
Metamathematics, $Th(\mathbf{K})$ , theory of $\mathbf{K}$       287
Metamathematics, $T^{'}_{klm}$ , modification of $T_{klm}$       298
Metamathematics, $T_{klm}$ , theory expressing the invariant (k, l. m)      292
Metamathematics, $\alpha_{kn}(x)$ , special formula      292
Metamathematics, $\lambda_{k}(x)$ , special formula      292
Metamathematics, $\mathbf{BA}$ , class of all BAs      288
Metamathematics, $\mathbf{BP}$ , class of all Boolean pairs      300
Metamathematics, $\mathbf{BP}^{*}$ , special members of $\mathbf{BP}$       300
Metamathematics, $\mathbf{BP}_{at}$ , special members of $\mathbf{BP}$       300
Metamathematics, $\mathbf{BP}_{rc}$ , members (A, B) of $\mathbf{BP}$ with B relatively complete in A      300
Metamathematics, $\mathbf{G}_{fin}$ , class of all finite graphs      302
Metamathematics, $\mathbf{K}^{'}\rightarrow_{sem}\mathbf{K}$ , $\mathbf{K}^{'}$ is semantically embeddable in $\mathbf{K}$       301
Metamathematics, $\phi(x_{1}\ldots x_{n})$ , free variables of $\phi$ are among $x_{1},\ldots, x_{n}$       288
Metamathematics, $\phi/\gamma$ , formula associated with $\phi$ , $\gamma$       291
Metamathematics, $\phi^{B}$ , relation defined by $\phi$ in B      301
Metamathematics, $\Sigma(x_{1}\ldots x_{n})$ , similarly for a set $\Sigma$ of formulas      288
Metamathematics, $\Sigma_{klm}(x)$ , special set of formulas      292
Metamathematics, $\varepsilon(x)$ , formula expressing E(A)      292
Metamathematics, $\varepsilon_{i}(x)$ , formula expressing $E_{i}$       292
Metamathematics, at(x), formula expressing that x is an atom      291
Metamathematics, atc(x), formula expressing that x is atomic      291
Metamathematics, atl(x), formula expressing that x is atomless      291
Metamathematics, CnS, set of consequences of S      298
Metamathematics, E(A), ideal formed for elementary invariants      288
Metamathematics, inv(A), elementary invariant of A      289
Metamathematics, Inv, set of elementary invariants      289
Metamathematics, Sent(L), set of all sentences of L      298
Metric space      65 236
Minimal completion      71
Monadic algebra      300
Monk's theorem on independence      206
Monk, J.D.      2 140 190 255 263 269 309f
Mono (morphism)      186
Monomorphism      29 66
Monotonicity laws      17
Normal $\kappa$ -Souslin tree      228ff
Normal form      47
Normal form for elements of a tree algebra      239 255 258
Normal form over X      51
Normal tree      226
Normed measure      233
Nowhere dense set in a space      28 182
Nowhere distributive      175
Number of filters      47 82
Number of ideals      127 139 145
Number of subalgebras      47 82
Number of ultrafilters      47 82
One-element BA      9
One-point compactification      103 115
Opposite partial ordering of a tree      226
Order topology      243ff
Order-preserving cardinal function      198
Orderings of a field      106
Ostaszewski, A.      271 310
Pairwise disjoint family      5 39f
Pairwise incomparable families      47 61f 253 see
Parovicenko, I.      95
Partial functions      55ff 214
Partial order      14 26f 55
Partial order of compactifications      116
Partial order topology      55 214
Partitions      38 41 88 225
Peirce arrow      27
Perfect kernel      274
Perfect representation      101 111
Pierce, R.S.      2 72 91 205 310
Positive element      28
Post, E.      3 310
Power set algebra      9 27 215
Preserving sums, products      36 59 102 125f
Prime filter      32
Prime ideal      76
Principal filter      31
Principal filter generated by a      31
Principal ideal      76
Product algebra      86 93 111
Product decomposition      47 86 179
Product of a subset      20ff
Product of BAs      7f 20 47 85 112ff 249 266
Projection in a vector space      23ff
Projection map      39 86
Projection map of a sheaf      117
Projective BA      124 139
Projective resolution      125
Projectivity      72
Proper filter      31
Proper ideal      76
Propositional logic      133 189 211
Pseudo-character      153ff
Quasi-order on compactifications      115

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