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| Enderton H.B. — Elements of set theory |
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| Предметный указатель |
Ordering of rational numbers 108
Ordering of real numbers 113
Orderings 39—40
Orderings, lexicographic 64 185 224
Orderings, linear 62 170
Orderings, partial 168
Orderings, total 62
Orderings, well 172
Ordinal numbers 8 15 182 189 191—194 249
Ordinal numbers, arithmetic of 227—239
Ordinal numbers, initial 199
Ordinal numbers, limit 203
Ordinal numbers, ordering of 192
Ordinal numbers, successor 203
Pair set 2 19
Pair set, ordered 35—36
Pairing axiom 18
Paradoxes 5 11 15 21 194
Partial ordering 168
Partial well ordering 245
Partition 55 57
Peano induction postulate 71
Peano system 70 76—77
Peano's postulates 70
Peano, Giuseppe 16 70
Perfect number 5
Permutation 144
Pigeonhole Principle 134
Pioneer 221
POSET 170
Positive 99 109
Power set 4 19 141
Power set axiom 18
pre 52
Primitive notions 11
proof 12 266
Proper class 6 15
Proper subset 85 134
Pure sets 9
Pythagoreans 111
Quadruples 42
Quantifiers 265
Quotient 58
Quotient field 107
RANGE 40
Rank 9 204 206 247—248
Rational numbers 102 121
Rational numbers, arithmetic of 103—110
Rational numbers, ordering of 108
Real numbers 113 121
Real numbers, arithmetic of 114—119
Real numbers, ordering of 113
Recursion 73
Recursion, transfinite 175 177 210 245
Reflexive 56
Regular 254 257
Regularity 8 205—206
Regularity axiom 15 84 206
Relation 40
Relation, binary 42
Relation, equivalence 56
Relation, n-ary 42
Relation, ordering 62
Relative complement 21 27
Relativization 250
Replacement axioms 15 179 253
Restriction 44 189
Richard, Jules 6
Ring 122 154
Russell's paradox 6 11 15 21
Russell, Bertrand 6 15 155 206 270
Schema 33 177
Schroeder — Bernstein theorem 147
Schroeder, Ernst 148
Segment 173
SEQUENCE 52 54 160 258
Set 1 6—8 11
Sierpiriski, Waclaw 270
Single-rooted 43
| Single-valued 42
Singleton 19
singular 257
SIZE 128
Skolem, Thoralf 15 270
smallest 171
Space-filling curves 149
Strong induction 87
Structure 170
Subsequence 259
Subset 3
Subset axioms 21
Subset, proper 85
Subtraction see Arithmetic
Subtraction theorem 235
Successor 68
Successor ordinal 203
Supremum 171 193 216
Supremum, strict 258 262
symmetric 56
Symmetric difference 32
Tarski, Alfred 256
Teichmuller — Tukey lemma 158
ternary 42
Theorem 12
Thread 54
Total ordering 62
Transcendental numbers 161 164
Transfinite induction 174 242
Transfinite induction, schema 200
Transfinite numbers 14 see Ordinal
Transfinite recursion 175 177
Transfinite recursion on ordinals 210
Transfinite recursion on well-founded relations 245
Transitive closure 178 244
Transitive extension 244
Transitive relation 56 243
Transitive set 71—73
Trichotomy 62—63 99 see
Triples 41
TRUE 250
Truth table 29 264
Truth value 264
Tuples 41 54
TYPE see Order type
Types (Russell) 206
unary 42
Undefined notions see Primitive notions
union 3 19 23
Union axiom 18 24
Union, indexed 51
Universal set 10 22
Upper bound 114 171
Use and mention 263
Vacuous truth 3 264
Value 43
van Heijenoort, Jean 270
Veblen theorem 218
Vector 58 153
Venn diagram 29
von Neumann-Bernays set theory 10 15
von Neumann. John 15 67
Well defined 18
Well founded 241—242
Well ordering 172
Well ordering by epsilon 191
Well ordering of natural numbers 86
Well ordering, partial 245
Well-ordering theorem 196
Wiener, Norbert 36
Word 160
Woset 172
Zermelo set theory 252
Zermelo — Fraenkel set theory 10 15 252
Zermelo, Ernst 6 15 67 270
Zero 203
Zero divisor 97 107
ZF see Zermelo — Fraenkel set theory
Zorn's lemma 151 153—154 195
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