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| Lightstone A.H., Robinson A. — Nonarchimedean Fields and Asymptotic Expansions |
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| Предметный указатель |
 77
 77
Absolute convergence 196
Absolute value 12
Archimedean property 7 9
Archimedean valuation 17
Archimedes 61
Asymptotic expansions 139 195
Asymptotic power series 144
Asymptotic sequences 138
Asymptotic series 141
Asymptotically equal functions 172
Asymptotically finite function 172
Atomic statement 41
Bellman, Richard 118
Bernoulli numbers 124
Bernoulli polynomials 124
Bolzano 61
Bourbaki, n 30
Cauchy product 25
Cauchy sequence 1 85
Cofinite subset 43
Compactness Theorem 36
Comparable sequences 167
Complete field 20
Completeness theorem 35
Constant function 29
Continuity 62
Continuity  107
Continuity at a standard number 61
Continuity, monadic 69
Continuity, q- 68 113
Continuity, s- 70 110
Continuity, sequential 107
Continuity, uniform 63
Convergence 20
Convergence in  175
Convergent sequence 19
Convergent Series 22
Copson, E.T. 151
Criterion for asymptotic expansions 141 154 156 171
Criterion for asymptotically finite functions 174
Criterion for convergence in 183
Criterion for convergence of series in 193
Criterion for equivalent functions 159
Criterion for iotas 94
Derivative 74
Derivative in  117
Diagonal relation 5
Dirac delta function 67 105
Dirac delta function, derivative 75 105
Elementary extension 49
Empty set requirement 43
Equality 4
Equivalence relation 4
Erdelyi, A. 195
Euclid 61
Eudoxus 61
Euler — maclaurin, approximation 129 130
Euler — maclaurin, expansion 129
Euler — maclaurin, formula 125 128
Euler — maclaurin, quadrature formula 123 124
Euler’s constant 131
Exponential integral function 118
EXTERNAL 39
External function 40
External language 42
External sequence 40
External statements 42
External subset 40
Field 8
Field,  31
Field,  35
Field, Archimedean 10
Field, complete 20
Field, hardy 29
Field, nonarchimedean 10
Field, ordered 9
Field, residue class 13 17
Fifth principle of permanence 97
Filter 43
Filter, empty set requirement 43
Filter, fixed 43
Filter, free 43
Filter, intersection requirement 43
Filter, maximal 45
Filter, superset requirement 43
Filter, ultrafilter requirement 44
Finite closed interval 63
Finite number 12
First principle of permanence 56
Fourth principle of permanence 97
Function 48
Function in a field 100
Function, asymptotically equal 172
Function, asymptotically finite 172
Function, constant 29
Function, continuous 61 62
Function, derivative 74
Function, Dirac delta 67 75
Function, exponential integral 118
Function, identity 12
Function, incomplete factorial 118
Function, polynomial 11
Function, standard 100
Fundamental theorem about finite numbers 39
Group of units 17
Group, abelian 5
Group, archimedean 5 8
Group, nonarchimedean 8
Group, ordered 7
Group, valuation 17
Hardy fields 29
Ideal 76
Ideal, maximal 76
Ideal, proper 76
Ideal, valuation 17
Identity relation 5
Incomplete factorial function 118
Infinite number 12
Infinite number, large 94
Infinitesimal 12
Infinitesimal, small 94
infinity 14
Internal 39
Internal function 40
Internal language 42
Internal sequence 40
Internal statement 42
Internal subset 40
Intersection requirement 43
Iota 94
| Jeffreys, harold and jeffreys, b.s. 118 121 125
Language, external 42
Language, internal 42
Laugwitz, d., v. 31
Laurent series 15
Levi-Civita, T. v 31
Lightsone, a.h. 39 120
Limit of convergent sequence 19 64
Lipschitz condition 102
Los’s lemma 49
Los’s lemma, proof 50—53
Many-sorted calculus 1
Many-sorted structures 1
Many-sorted structures, language 1
Maximal 45
Maximal filter 45
Maximal ideal 76
Mega 94
Metric 18
Metric space 19
Monad 13
Monadic continuity 69
Nonarchimedean field 10
Nonarchimedean group 8
Nonarchimedean valuation 14 18
Nonstandard criterion for asymptotic expansions 156
Nonstandard criterion for convergence in 183
Norm 180
Norm on 180 187
Number, bernoulli 124
Number, finite 12
Number, infinite 12
Number, infinitesimal 12
Number, natural 48
Number, real 48
Number, standard part 39
One-sorted system 3
Ordered group 7
Ordered set 6
Ostrowski, A. v 31
P-series 90
Peano’s induction postulate for 40
Peano’s induction postulate for  56
Poincare, H. 137
Polynomial Bernoulli 124
Polynomial degree 11
Polynomial function 11
Popken, J. 172 187
Principle of mathematical induction for 40
Principle of mathematical induction for 58
Principle of permanence 56
Principle of permanence, fifth 97
Principle of permanence, first 56
Principle of permanence, fourth 97
Principle of permanence, second 57
Principle of permanence, sixth 98
Principle of permanence, third 57
Proper ideal 76
Q-continuity 68 113
Relation, diagonal 5
Relation, equality 4
Relation, equivalence 4
Relation, identity 5
Relation, irreflexive 6
Relation, substitutive 4
Relation, total 6
Relation, transitive 6
Residue class field 13 17
Ring of cosets 77
Ring, valuation 17
Robinson, Abraham 30 39 53 79
S-continuity 70 110
Second principle of permanence 57
Seq-continuity 107
SEQUENCE 19 48
Sequence, asymptotic 138
Sequence, comparable 167
Sequence, convergent 19 175
Sequence, gauchy 1 85
Sequence, limit 19 64
Sequence, sum 25
Sequentially comprehensive 55
Sequentially continuous 107
Series,  90
Series, asymptotic 141
Series, asymptotic power 144
Series, cauchy product 25
Series, convergent 22
Series, Laurent 15
Series, sum 64
Set, basic 3
Set, ordered 6
Set, supporting 2
sgn 126
Sixth principle of permanence 98
Standard map 48
Standard object 48
Standard part 39
Statement 41
Statement, atomic 41
Statement, external 42
Statement, false 42
Statement, internal 42
Statement, length 50
Statement, true 42
Stirring’s formula 136
Stokes’ phenomenon 151
Subset 48
Subset, cofinite 43
Substitutive relation 4
Superset requirement 43
Supporting set 2
Third principle of permanence 57
Transfer theorem 37
Triangle inequality 12 18
Trichotomy Law 6
Ultrafilter requirement 44
Ultrametric inequality 19
Ultrapower theorem 49
Uniform continuity 63
Valuation, archimedean 17
Valuation, group 17
Valuation, ideal 17
Valuation, nonarchimedean 14 18
Valuation, p-adic 15
Valuation, ring 17
Valuation, trivial 15
van der Corput, J.G. 137 172 195
VS 48
Watson’s lemma 162
Weierstrass 61
Zorn’s Lemma 45
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