Smullyan R.M. — Godel's incompleteness theorems :: Электронная библиотека попечительского совета мехмата МГУ

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Smullyan R.M. — Godel's incompleteness theorems

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Название: Godel's incompleteness theorems

Автор: Smullyan R.M.

Аннотация:

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1992

Количество страниц: 139

Добавлена в каталог: 25.10.2005

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Предметный указатель

      69
      69
$(\exists v_i \leq c)F$       41
$(\exists v_i \leq t)F$       17
$(\forall v_i \leq t)F$       17
$(\forall x \in y)$       33
$E [\bar{n}]$       25
      23
$K_{11}$       32
      36
      36
$x \in y$       32
$x \prec_z y$       32
$\ell (n)$       21
$\ell_b (n)$       21
$\leftrightarrow$       6
$\mathcal{N}$       57
$\omega$ -consistent      57
$\omega$ -incompleteness      73
$\omega$ -inconsistent      56
$\omega$ -rule      113
$\Pi (x,y,z)$       87
$\Sigma _0$ -complete      66
$\Sigma _0$ -formulas      41
$\Sigma _0$ -relations      41
$\Sigma _1$ -formula      42
$\Sigma _1$ -formulas and relations      42
$\Sigma _1$ -relations      42
$\Sigma$ -formulas      42
(Q)      68
(R)      69
A*      6 26
Abstract forms of Goedel’s and Tarski’s theorems      5
Arithmetic (note the capital “A”)      19
Arithmetic (note the small “a”)      19
Askanas’ theorem      114
Axiomatizable      57
Carnap’s rule      113
Complete representability      97
Concatenation to the base b      20
Consis      108
Constructive arithmetic relations      41
Correctly decidable      66
D(X)      6 26 102
Degree      16
Designation      17
Diagonal function      26 102
Diagonalizable      108
Diagonalization      6 24 26
eet      132
Express      19
Expressibility      5
Expressible      6
Extension      57
Fixed point      102
Formation sequence      33
Goedel numbering      22
Goedel sentences      8 24
Goedel — Rosser incompleteness theorem      76

Goedel’s incompleteness theorem for P.E.      36
IFF      6
Kripke, Saul      46
Language $\mathcal{L}_E$       14
Myhill, John      43
Nameable      6
neg(x)      34
P*      59
P.A.      40
P.E.      28
Peano arithmetic      40
Peano Arithmetic with exponentiation      28
Provability predicates      106
r(x,y)      25
R*      59
R.e. systems      57
Recursive relations      98
Recursive set      98
Recursively axiomatizable      57
Regular formula      16
Represent      58
Representation function      26
Robinson, Raphael      69
Rosser system      78
Rosser system for n-ary relations      78
Rosser system for sets      78
Rosser’s undecidable sentence      81
S(X)      34
Sb(s)      34
Separability      77
Separates      77
Separation lemma      79
Seq(x)      32
Sequence number      32
Shepherdson’s representation lemma      88
Shepherdson’s representation theorem      86
Shepherdson’s separation lemma      91
Simply consistent      56
Strong definability of functions in $\mathcal{S}$       98
Strong separation      87
Strongly separates      87
Subsystem      57
Superset      12
system ()      69
system (Q)      69
system (R)      69
Tarski’s rule      113
Tarski’s theorem      24 27
Truth in $\mathcal{L}_E$       17
Truth predicates      104
Undecidable sentences      10
Var(x)      34
Weak separation      87
Weakly separates      87
x exp y      34
x id y      34
x imp y      34
x le y      34
x pl y      34
x tim y      34

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