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| Enderton H.B. — Elements of set theory |
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| Предметный указатель |
Abelian group 95 122
Absolute value 109 118
Absorption law 164
Abstraction 4—6 20—21 30 37
Addition see Arithmetic
Additive inverse 95 104 117
Aleph 137 212
Algebra of sets 27—31
Algebraic numbers 161
Antinomies see Paradoxes
Archimedean 120
Arithmetic of cardinal numbers 138—143 149 164
Arithmetic of integers 92—100
Arithmetic of natural numbers 79—82 85
Arithmetic of order types 222—226
Arithmetic of ordinal numbers 227—239
Arithmetic of rational numbers 103—110
Arithmetic of real numbers 114—119
Associative laws 28 see
Atomic formula 263
atoms 7—9 13
Aussonderung axioms 15 21 see
Axiom of Choice see Choice axiom
Axiomatic method 10—11 66 125
Axioms of set theory 15 166 271—272 see
Bar-Hillel, Yehoshua 269
Bernays, Paul 15
Bernstein's theorem 147
Bernstein, Felix 148
Berry paradox 5
Berry, G. 6
Beth 214 254
Binary operation 79
Binary relation 42
Borel, Emile 148
Bound 114 171
Bounded 114 212
Burali-Forti theorem 194
Burali-Forti, Cesare 15 194
Burrill, Claude 112
Cancellation laws for cardinal numbers 141
Cancellation laws for integers 100
Cancellation laws for natural numbers 86
Cancellation laws for ordinal numbers 234
Cancellation laws for rational numbers 110
Cancellation laws for real numbers 118
Canonical map 58
Cantor Normal Form 238
Cantor — Bernstein theorem 148
Cantor's theorem 132 261
Cantor, Georg 14—15 112 148 166 269—270
Cardinal comparability 151
Cardinal numbers 136—137 197 221
Cardinal numbers, arithmetic of 138—143 149 164
Cardinal numbers, ordering of 145
Cardinality 137
Cartesian product 37
Cartesian product, infinite 54
Cauchy sequence 112
Chain 151
Chain, descending 173
Characteristic function 131
Choice axiom 11 49 55 151—155 198
Choice function 151
class 6 10 15 20
Closed 68 70 107 216
Closure 78
Closure, transitive 178 244
Cofinal 257
Cofinality 257 260
Cohen. Paul 166 269
Commutative diagram 59
Commutative laws 28 see
Commutative ring 122
Comparability 151
Compatible 60
Complement 27 see
Complete ordered field 119
composition 44
Comprehension see Abstraction
Connected 63
Constructed 175—177 180 211
Constructive method 66 125
Constructivity 154
continuous 216
Continuous functions 165
Continuum Hypothesis 165 215
Continuum hypothesis, generalized 166 215
Contradiction, proof by 265
Contrapositive 265
Converge 259
Coordinate 37 54
Coordinate plane 40
Corners 263
Correspondence 129
Countable 159
Counterexample 87 265
Counting 136 197
Cut 112—113
De Morgan's laws 28 31 264
Dedekind cut 112—113
Dedekind, Richard 14 70 157 270
Defined terms 23 267
Denominator 102
Dense 111 227
Derived operation 219
Descartes, Rene 37
Descending chain 173
Difference 50 91 see
Disjoint 3 57
Distributive laws 28 see
Divisibility 40 167
Division 107
Division theorem 236
Domain 40
Dominate 145
Drake, Frank 269
Element 1
Embedding 100
Empty set 2
Empty set axiom 18
End extension 230
Enderton. Herbert 12
EPSILON 16
Epsilon numbers 240
Epsilon ordering 191
Epsilon-image 182
Equality 2
Equinumerous 129
Equivalence class 57
Equivalence concept 132 186
Equivalence relation 56
Euler, Leonard 43
Even 83
Exhaustive 57
exponentiation see Arithmetic
Extension 125
Extensional 125
Extensionality 2 12 13 17 52
Factorial 144 165
Field of set 40
Field, algebraic 107 122
Field, algebraic, ordered 109 119 123
finite 133 157
Finite, cardinal 137
Fixed point 54 218
Formula 22—23 263—265
Formula, atomic 263
Foundation axiom see Regularity axiom
Foundations of mathematics 10—12 15 123—127 250
| Fourier series 14
FRACTION 102
Fraenkel, Abraham 15 269 270 see
Frege, Gottlob 6 15 124—125 270
Function 42—43
Function, multiple-valued 44
Function-class 176 179
Fundierungsaxiom see Regularity axiom
Galileo Galilei 131
Gleason, Andrew 119
Godel's second incompleteness theorem 250 256
Godel, Kurt 15 166
Godel-Bernays set theory 15
Graph 39 42
GREATEST 171
Greatest common divisor 172
Greatest lower bound 171
Grounded 204
Group 122 154
Group, abelian 95 122
Hamilton. Norman 113
Hartogs' theorem 195
Hausdorff, Felix 153
Hebrew lexicographic order 224
Hereditarily finite 256
Hilbert, David 166
Historical notes 6 11 14—16 36 43n 67 70 111 112 124 131 148 153 154 166 194 206 256
honesty 124
Identity element 94—95 97 106 116 119 226 229
Identity function 40 47
Identity Principle 2
IFF 2
Image 44 50.
IMPLY 264
Inaccessible 254—256
Inaccessible, weakly 258
inclusion 3
Inclusion, proper 85 167
Increasing 259 see
Index set 51 54
Induction 69
Induction, strong 87
Induction, transfinite 174 200 242
Inductive 68 174
Infimum 171
Infinite 15 133 157
Infinite, cardinal 137
Infinity axiom 68
Initial ordinal 199
Initial segment 173
Injection 43
Integers 75 92 121
Integers, arithmetic of 92—100
Integers, ordering of 98
Integral domain 97 122
Intensional 125
Intersection 3 21 24—25
Intersection, indexed 51
interval 44 130
INTO 43
Inverse 44 46 see Multiplicative
Inverse image 45 51
Inverse, left 48
Inverse, right 48
Irreflexive 63
Isomorphic 77 184
Isomorphic embedding 100 110 119
Isomorphism 184 186
Isomorphism type 207 221
Jech, Thomas 270
Jourdain, Philip 269
Konig's theorem 261
Konig, Denes 249
Konig, Julius 262
Kronecker, Leopold 14
Kuratowski, Kazimierz 36 153 270
Landin, Joseph 113
Language of set theory see Formula
Large cardinal axiom 256
Largest 171
LEAST 87 171
Least common multiple 172
Least upper bound 114 171 see
Length 160
Less than 83
Levy, Azriel 269
Lexicographic ordering 64 185
Lexicographic ordering, Hebrew 224
Limit ordinal 203
Linear algebra 58 153
Linear ordering 62 170
Logarithm theorem 237
Logic 12 186 263—267
Logical consequence 12
Logicism 15
Loset 170
Lower bound 171
MAP 43
Mathematics 126
Maximal 151 171
Maximum 171
Measurement 136 187 220
Member 1 11
Mendelson, Elliott 119
Metamathematics 16 166 253
Minimal 170 241
Minimum 171
Mirimanoff, Dmitry 15 206
Model 250
Monotone 216 see
Monotonicity 30
Mostowski, Andrzej 270
Multiplication see Arithmetic
Multiplicative axiom 151
Multiplicative inverse 102 107 119
n-ary relation 42
n-tuples 41
Naive set theory 11
Natural map 58
Natural numbers 21 66 68
Natural numbers, arithmetic of 79—82 85
Natural numbers, ordering of 83
Neumann, John von see von Neumann John
normal 216
Notation 13 see
Number, concept of 123—127
Numbers see Cardinal numbers. Integers Natural Ordinal Rational Real
Numeration theorem 197
Numerology 5
Odd 83
One-to-one 43
One-to-one correspondence 129
Onto 43
Operation on ordinals 215—216
Operation, binary 79
Order type 189 222 see
Order type, arithmetic of 222—226
Order-preservation in arithmetic for cardinal numbers 149
Order-preservation in arithmetic for integers 99
Order-preservation in arithmetic for natural numbers 85
Order-preservation in arithmetic for ordinal numbers 234
Order-preservation in arithmetic for rational numbers 109
Order-preservation in arithmetic for real numbers 118—119
Ordered field 109 119 123
Ordered n-tuples 41—42
Ordered pair 35—36
Ordering of cardinal numbers 145
Ordering of integers 98
Ordering of natural numbers 83
Ordering of ordinal numbers 192
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