 -Kochen ring 102
 -saturated 62
 - group 9 85
 -adic Kochen operator 122
-adic Kochen operator of type (e, f) 95
(relative) initial index 23 94
Absolute value 1
Algebraic Embedding Theorem 53
Artin 2
Ax 5
Axiom, universal 83
Base field 93
Basic subset 125
Bezout ring 117
Canonical decomposition 24
Center 100
Characterization Theorem, p-adic 9
Characterization Theorem, real 4
Coarse valuation 25
Completeness 89
Convex subgroup 14
Core field 26
Core valuation 27
Decidability 5 87 89
Decomposition, canonical 24
Defect 29
Defining relation 52
Definite, integral 123 144 149
Definite, positive 2
Dimension (of a place) 123
Eisenstein polynomial 39
Elementary equivalence theorem 90
Elementary extension 86
Embedding Theorem for regular extensions 65
Embedding Theorem, Algebraic 53
Ersov 5
Formally p-adic 7 92
Formally p-adic of type (e, f) 93
Formally p-adic over 93 125
Formally real 4 92
General Embedding Theorem 63
Hensel's lemma 8 20
Henselian 20
Henselization 21
Hilbert's  Problem 2
Holomorphic at 134
Holomorphy ring 104 134
Immediate extension 21
Initial index 23 94
Integral definite 123 144 149
Isomorphism Theorem for algebraic extensions 57
Isomorphism Theorem for p-adic closures 9
Isomorphism Theorem for real closures 4
Kochen 5
Kochen operator 8
Kochen operator, -adic 95 122
Kochen operator, -adic of type (e, f) 95
Kochen operator, p-adic 92
Kochen ring over 135
Kuhlmann 142
Language of valued fields 83
Language, modified 84
Laurent series (formal) 16
Level of a unit 45
lexicographical ordering 15
MacIntyre 91
McKenna 149
Merckel's Lemma 102 135 153
Model completeness (of real closed fields) 5
Model Completeness Theorem 86
Modified language 84
Nakayama's lemma 111
Newton's Lemma 20
Non-principal ultra filter 18
Nullstellensatz 143
Ordering 2
p-adic Analog of Hilbert's Problem 148—149
p-adic closure 8 33
| p-adic Kochen operator of type (e, f) 92
p-adic topology 124
p-adic transfer principle 10
p-adically closed 8 33 84
p-divisibility 6
p-ramification index 13
p-rank 13 83
p-valuation 7
p-valuation of type (e, f) 93
p-valued field 7
p-valued field of p-rank d 13
Place Existence Theorem 125
Place, rational 124
Positive definite 2
Prime element 13
Principal ideal theorem 118
Pruefer ring 117
Puiseux series 16
Quantifier Elimination Theorem 91
Radical element 48
Radical group 48
Radical Structure Theorem 48
Ramification, p-ramification index 13
Ramification, relative ramification index 23
Rational place 124
Real closed 4
Real closure 4
Regular extension 64
Relation, defining relation 52 112
Relative residue degree 94
Relative type 94
Residue degree 15
Riemann space 124
Ring, -Kochen ring 102
Ring, Bezout ring 117
Ring, holomorphy ring 104 134
Ring, Kochen ring 135
Ring, Pruefer ring 117
Rule 11
Schreier 4
Sign function 76
Spectral Structure Theorem 114
Subfield Structure of the p-adic closure 59
Substructure completeness 91
Tarski's transfer principle 5
Teichmueller representative set 39
Theorem, Algebraic Embedding Theorem 53
Theorem, Characterization Theorem (p-adic) 9
Theorem, Characterization Theorem (real) 4
Theorem, Elementary Equivalence Theorem 90
Theorem, Embedding Theorem for regular extensions 65
Theorem, General Embedding Theorem 63
Theorem, Isomorphism Theorem for algebraic extensions 57
Theorem, Isomorphism Theorem for p-adic closures 9
Theorem, Isomorphism Theorem for real closures 4
Theorem, Model Completeness Theorem 86
Theorem, Nullstellensatz 143
Theorem, p-adic Analog of Hilbert's Problem 148—149
Theorem, Place Existence Theorem 125
Theorem, Principal Ideal Theorem 118
Theorem, Quantifier Elimination Theorem 91
Theorem, Radical Structure Theorem 48
Theorem, Subfield Structure of p-adic closure 59
Totally positive 3
Transfer principle, p-adic 10
Transfer principle, Tarski's 5
Type (e, f) 92 93
Ultra-filter 18
Ultra-power 17
Uniqueness of p-adic closure 37
Unit, level of a unit 45
Universal axiom 83
Valuation, p-valuation 7
Valuation, p-valuation of type (e, f) 93
Zariski topology 124
Zariski's Local Uniformization 142
Zariski-dense 145
Zero support 18
|
|
|
О проекте