Alling N.L. — Foundations of Analysis over Surreal Number Fields :: Электронная библиотека попечительского совета мехмата МГУ

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Alling N.L. — Foundations of Analysis over Surreal Number Fields

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Название: Foundations of Analysis over Surreal Number Fields

Автор: Alling N.L.

Аннотация:

In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway's field of surreal numbers is also given.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1987

Количество страниц: 373

Добавлена в каталог: 02.02.2010

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

Предметный указатель

Order (of a formal power series)      7.40
Order (of a root)      1.72
Order axiom (= (0))      4.60
Order valuation      6.00
Order-isomorphic      1.01
Order-preserving      1.60
Order-type      1.01
Ordered abelian group      1.60
Ordered class      1.10
Ordered direct sum (of groups)      1.60
Ordered direct sums (in $\xi H$ )      1.65
Ordered field      1.70
Ordered group      1.60
Ordered ring      1.70
Ordered set      1.01
Ordered subset      1.10
Ordering      1.10
Ordinal number      1.02
P(u,v:w,z) (= an order property)      4.05 4.06
Partial sums (of $\omega$ -power series)      6.43
Place (associated with a valuation)      6.00
Point of stability      5.51
Positive element (in a ordered group, ring or field)      1.60 1.70
Positive regular index (= pri)      1.30
Possibly untimely (cut representation)      4.09
Power (of a set - its cardinal number)      1.03
Predecessor      4.50 4.51 4.53
Predecessor cut representation      4.54
Preserves $\leq$       1.01
Preserves <      1.01
pri (= positive regular index)      1.30
Prime disk of hyper-convergence (a)      7.84
Prime disk of hyper-convergence (the)      7.92
Prime ideal in a valuation ring      6.70
Prime polydisk of hyper-convergence      7.84
Principal convex subgroup      1 .60
Principal interval      1.10
Pseudo-convergent sequence      1.62 6.40
Pseudo-limit (a)      1.62 6.40
Pseudo-limit (the)      6.41 6.42
Q (= rational field)      1.20
Q(u,v;w,z:x,y) (= an order property)      4.05
Quadratic term (of a formal power series)      7.40
RADIUS      4.21
Rank (- p)      5.40
Rational (cut)      1.20
Real (numbers R in No)      4.30
Real-closed field      1.71
Reduced form      4.21
Refinements (of Conway cuts)      4.09
Region of hyper-convergence      7.22
Regular (cardinal number)      1.30
Relativ $\xi$ -open      2.12
Relativ $\xi$ -topology      3.20
Relative $\xi$ -closed      2.12
Relative maximum      1.74
Relative minimum      1.74
Relative topology      1.11
Represents (an element)      4.02
Residue class field      6.00
Right character      1.30
Right-option      4.00
Ring of finite elements      6.00
Rolle's theorem      1.74
Root-closed field      7.33
Secant (over certain formal power series fields)      7.50
Second'Derivative Test      1.74
Section (of an ordered class)      1.02

Semi-algebraic set      3.00
Sequence (in a set)      7.21
Set theory      1.00
Sign-expansion (function $\sigma$ )      4.50
Simple density axiom (= (SD))      4.60
Simple zero      1.73
Simpler (= of $\leq$ birthday)      4.01
Simplest Dedekind-completion      5.50
Sine (= extended sine function over $\xi Cx$ )      7.51
Sine (over certain formal power series fields)      7.50
Singular (cardinal number)      1 .30
Skeleton (of an ordered group)      1.63
Stable value      5.51
Strictly decreasing (sequence)      7.21
Strictly increasing (sequence)      7.21
Strictly positive element (in an ordered group, ring or field)      1.60 1.70
Strictly-order-preserving (mapping)      1.01 1.60
Strictly-order-reversing (mapping)      1.01
Strong topology      3.00
Strongly inaccessible (cardinal number i)      5.40
Subsequence      7.21
Subtraction (in No)      4.04
Successor      4.50 4.51 4.53
Support      1.63 6.20
Surcomplex number fields (Cx, and $\xi Cx$ )      7.10
Surjection      (= a map of one set onto another)
Surjective      (= a mapping that is a surjection)
Surreal monomorphism      4.03
Surreal number fields (No, and $\xi No$ )      5.00
Sylow theorems      1.71
symmetric      4.21
Tangent (over certain formal power series fields)      7.50
Tarski — Seidenberg theorem      3.00
Taylor — Neumann series      7.91
The canonical direct summand      1.65
The limit (of a pseudo-convergent sequence)      1.64 6.41 6.42
Timely (cut representation)      4.02 4.09
Topological field (under the $\xi$ -topology)      3.40
Totally ordered set (-ordered set)      1.01
Transfinite induction      1.02
Tree order      4.50 4.51.
Triangle equality      1.61
Triangle inequality      1.61
True $\eta$ -character      1.40
U (= group of units of a valuation ring 0)      6.00
U(g)      3.00
UCF (universal choice function axiom)      1.00
Universally embedding      6.60
Universes (in set theory)      5.40
Upper character      1.30
Upper-saturated      1.30
V (= valuation)      6.00
Valuation ring      6.00
Valuation topology      7.62
Valuation topology and the interval topology      7.63
Value group      6.00
Value set      1.61
VS (= value set)      1.61
W(G)      3.00
Weak $\xi$ -topology      2.01
Weakly inaccessible (cardinal number)      1.30
Well-ordered (class)      1.02
Z(G)      3.00
Z-module      (= module over the ring Z)
Zero of order n      1.73
ZF (set of axioms)      1.00
ZF + С (set of axioms)      1.00
Zorn's lemma      4.61
|      (= operator that restricts a function)

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