Index 187
semi-norm, 150
splitting axiom, 153
standard, 20
standard part, 21, 138
standard universe, 131
strong arithmetic regularity lemma, 91
structure and randomness, 34
superstructure, 131
symmetric polynomial, 80
syndeticity, 19
Taylor coefficient, 98
tensor product, 151
total asymptotic equidistribution, 4, 10
total equidistribution (ultralimit
analysis), 22
transference, 110
triangle inequality, 149
ultralimit, 20, 21, 134
ultrapower, 20, 134
ultraproduct, 20, 134
van der Corput inequality, 7
van der Corput lemma, 8, 11, 24, 65
vertical character, 103
vertical frequency, 103
Vinogradov lemma, 15, 24
von Mangoldt function, 124
weight function, 112
Weyl criterion, 13
Weyl equidistribution criterion, 5, 10,
13, 23, 64
Weyl equidistribution theorem, 9
Weyl law, 173
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