Truss J. — Foundations of mathematical analysis :: Электронная библиотека попечительского совета мехмата МГУ

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Truss J. — Foundations of mathematical analysis

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Название: Foundations of mathematical analysis

Автор: Truss J.

Аннотация:

Foundations of Analysis covers a variety of issues that will interest undergraduates and first-year graduate students studying pure mathematics and philosophy. It covers the development of different number systems and how their consideration leads to specific branches of mathematics.

Язык:

Рубрика: Разное/

Статус предметного указателя: Готов указатель без номеров страниц

ed2k: ed2k stats

Год издания: 1997

Количество страниц: 363

Добавлена в каталог: 12.03.2015

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID

Предметный указатель

Disconnected      106
Discontinuity      97
Discontinuous function      319
Discrete metric space      122
Discrete topology      108 234
Disjoint      184
Dissection      150 270
Distance      106 121
diverge      73 137 163
Divide      64
Divisibility      54 50
Divisibility test      72 77
Division      16 54
Domain      3
Double integral      269
Downward Loewenheim — Skolem theorem      301
Downwards closed      98
duplicate      111
EDGE      252
Effective      23 258 327
Effective computability      49
Effective enumeration      292
Effective open set      291
Effective procedure      12
Effective union      292
Element      2
Elementary submodel      304
Elementary symmetric function      196 216
Embedding      45 99 257
Empty set      0 2 6
End-extension      119
Endpoint      92 104
Enumeration      24
equation      95
Equipollent      4 34
Equivalence class      3
Equivalence relation      3
Error      224
Essentially second order      112
Essentially undecidable      20
Euclid      7 262
Euclid's Algorithm      53 56
Euclid's Elements      55 110
Euclidean distance      123
Euclidean Domain      53 55 58
Euclidean geometry      83
Euclidean metric      122
Euclidean topology      108
Eudoxus      110
Euler's constant      218 221
Euler's identity      176
Even function      168
Even integers      65
Even permutation      185
Event      262
Eventually      153
Eventually periodic      74
Exchange property      219
Existence      39 258
Existential quantifier      12 292 308
Exponential      164 176
Exponential function      105
exponentiation      10 164
Exponentiation of cardinals      34
Extended Dedekind cut      100
Extended formal power series      205
Extended order-completion      100
Extended real line      100 134
Extension      172 303
Extensional      2 319
Exterior approximation      263
Face      252
Factor      53
Factor group      182
Factor out      45
Factor ring      61
Factorial      91
Factorization      53
Fan Theorem      333
Fermat's last theorem      58 311
Ferrari      193
Field      63 65 101 177
Field extension      63 177
Field of algebraic numbers      204
Field of fractions      64 139 205
Field of rational functions      87 190
Filter      134 145 303 329
Fine structure of the constructible hierarchy      300
Finitary      1
Finite cardinal      6
Finite character      83 219
Finite continued fraction      243
Finite description      308
Finite extension      49
Finite field      86
Finite field extension      177
Finite intersection property      145 329
Finite metric space      122
Finite ordinal      28
Finite sequence      27
First category      258
First isomorphism theorem      328
First isomorphism theorem for groups      182
First Isomorphism Theorem for rings      62
First order      8
First order definable      299
First order language      112
First order sentence      113
First order theory      220
First principles      153
Fixed field      191
Fontana      193
Forcing      47 117 301
Forcing language      305
Forcing relation      305
Formal Arithmetic      12 299
Formal language      12
Formal polynomial      86
Formal power series      162 205
Formalization      1
Formula      12 328
Forth      93
FRACTION      64
Fractional power      158
Fractional power series      173 203 205
Fraenkel      5
Free variable      13 329
Frege      1 5
Frege — Russell      1 5 22
Frontier      249
Fubini      275
Fubini's theorem      289 274
Function      3
Function symbol      329
Fundamental theorem of algebra      173 200
Fundamental Theorem of Arithmetic      58 208
Fundamental theorem of calculus      154 158
Fundamental Theorem of Galois Theory      191
Galois      188 193
Galois group      191
Galois group of a polynomial      193
Galois theory      173 181
Game      284
Gap      95 136
Gauss      173 200
GB      6
Gelfond — Schneider theorem      218
Generalized Continuum Hypothesis      300
GENERATED      43
GENERIC      302

Generic Extension      305
Generic filter      303
Geometric progression      73 115
Geometry      7 83 121
global      140
Godal number      18
Goedal's completeness theorem      30
Goedel      6 12 296
Goedel's constructible sets      288
Goedel's incompleteness theorems      19 21 30 288 304
Goedel's theorems      16
Goedel's undecidable sentence      312
Goedel's — Bernays      6
Gradient      69
Graph      95
Greatest common divisor      56
Greatest lower bound      97
Ground model      287
Group      38
Group of units      53
Group theory      35 173 181
Hahn — Banach theorem      332
Halpern      334
Hamal basis      210
Hardy      201
Harmonic series      127 183
Hausdorff      145 298
HCF      56
Heine — Borel theorem      143 146
Her mite      214
Heyting      308
Heyting algebra      321 328
Heyting arithmetic      312
Hierarchy      291
Highest common factor      53 56
Highly homogeneous      249
hilbert      17 21 326
Hilbert's Programme      17
Hodges      332
Homeomorphism      232
Homomorphism      38 61 80 182
Horizontal section      278
Hyperarithmetic hierarchy      293
Hyperbolic function      170
Ideal      58 140 279 328
Ideal of meagre sets      279
Ideal of null sets      279
Identity      36
Identity function      102 155
Identity permutation      184
Imaginary      172
Imaginary axis      175
Imaginary part      175
Immediate predecessor      235
Immediate successor      235
Implicit differentiation      156
Inaccessible cardinal      287
inclusion      99
Inclusion map      129
Incompleteness theorems      19 21
Inconsistent      17
Increasing sequence      128
Independence of the continuum hypothesis      301
Independence proof      304
Independent      83 117 209 288
Indeterminate      11 101 173 176
INDEX      42
Induction      10 30
Induction step      9
inf      97
Inference rule      13
Infimum      97
Infinitary combinatorics      288
Infinite cyclic group      43
Infinite decimal      72 133
Infinite gap      23 31
Infinite intersection      25
Infinite model      220
Infinite search      19
Infinite series      162 224
Infinite union      25
Infinitesimal calculus      148
Infinitude of the set of primes      30 214
Infix notation      3
Initial ordinal      35
Inner approximation      149
Inner Lebesgue measure      265
Inner measure      269
Inner model      299 301
Inscribed polygon      148
Insoluble      186
INTEGER      38
Integer matrix      51
Integer polynomial      211
integral      151
Integral domain      50 64 205
Integration      147 153 269
Intensional      319
Interior      107
Interior approximation      263
Intermediate Value Theorem      95 104 135 319
Intersection      2
interval      107
Intuitionism      135 211 308
Intuitionistic arithmetic      312
Intuitionistic logic      328
Intuitionistic semantics      321
Inverse      38
Inverse function      157 167
Inverse image      143
Inverse operation      64 153 158
Inverse trigonometric function      228
inversion      242
Irrational      111 318
Irrational cut      133
Irrational number      100 205
Irrationality of $\pi$       215
Irrationality of e      213
Irreducible      53 174
Irreducible polynomial      177
Irreflexive      24
Irreflexive ordering      24
Isolated      247 276 289
Isometry      122
Isomorphic      39 65 85
Isomorphism      8 38 65 85 98 182
Isosceles triangle      148
Iterated derivative      213
Iterated forcing      334
Iteration      224
Jensen      300 334
Jordan curve theorem      202
Kernel      61 182 328
Koch snow-flake curve      159
Kolmogorov      278
Konig's tree lemma      118 332
Kripke model      312
Kummer      58
Kuratowski — Ulam      283
Label      47
Lachlan      220
Lagrange's theorem      42
Language of arithmetic      292
Large Cardinals      288
Lattice pattern      47
Lattice point      69
Lauechli      332
Law of excluded middle      310
Lawlike sequence      314
Laws of indices      164

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