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Manin Yu.I. — A Course in Mathematical Logic
Manin Yu.I. — A Course in Mathematical Logic

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Название: A Course in Mathematical Logic

Автор: Manin Yu.I.

Аннотация:

This book is a text of mathematical logic on a sophisticated level, presenting the reader with several of the most significant discoveries of the last 10 to 15 years, including the independence of the continuum hypothesis, the Diophantine nature of enumerable sets and the impossibility of finding an algorithmic solution for certain problems. The book contains the first textbook presentation of Matijasevic's result. The central notions are provability and computability; the emphasis of the presentation is on aspects of the theory which are of interest to the working mathematician. Many of the approaches and topics covered are not standard parts of logic courses; they include a discussion of the logic of quantum mechanics, Goedel's constructible sets as a sub-class of von Neumann's universe, the Kolmogorov theory of complexity. Feferman's theorem on Goedel formulas as axioms and Highman's theorem on groups defined by enumerable sets of generators and relations. A number of informal digressions concerned with psychology, linguistics, and common sense logic should interest students of the philosophy of science or the humanities.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1977

Количество страниц: 286

Добавлена в каталог: 31.03.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$L_1Ar$      6
$L_1Set$      6
$L_2Real$      109
$V^{B'}$      121
$\mu$-operator      182
Absolute      65 155
Admissible      93 104 235
Algorithmically decidable      183
Alphabet      3
atomic      7
Axiom of Choice      47 135
Axiom Schema      43
Benign (subgroup)      270
Big class      151
Boolean algebra      54
Boolean truth function      55 120
Bounded      273
Cardinality      103
Characteristic function      179
Church's thesis      181
Closed      24
Codimension      191
Cofinality      148
Cohen forcing      55 143ff
Compatible (numberings)      234
composition      181
Computable      178
Consistent      58
Constant      7
Constructible      150 167
Continuum Hypothesis      105
Decidable      198
Diophantine      206
Disjoint      146
Display      79
Effective (numbering)      152
Expression      3
Family      101
Finitely generated      262
Finitely presented      262
First order language      6
Formula      7
free      23
Gen (generalization)      30
General recursive      183
Generalized Continuum Hypothesis      160
GENERIC      145
Goedel numbering      242
Goedel's completeness theorem      39 58
Goedel's incompleteness theorem      81 239
Goedelian (set of formulas)      32
Hereditarily finite      45
Higher order languages      15
Hilbert's tenth problem      208
Inaccessible cardinal      46
Inconsistent      58
Internal, model      171
Interpretation      24
Juxtaposition      182
Kenning      56
Kolmogorov's complexity theorem      226
Label      79
Language      3
Level set      190
Loewenheim — Skolem theorem      65
Logical polynomial      30
Mapping      25
Mass problem      183
Metalanguage      4
Model      26
Modular structure      92
MP (modus ponens)      30
NAME      9
Normal models      43
Numbering      233
Occurrence      20
Ordinal      96
Parentheses bijection      21
Partial Boolean algebra      89
Partial function      178
Partial ordering      96
Partial recursive      183
Primitive enumerable      191
Primitive recursive      183
proof      48
Q-absolute      171
Quantum logic      87
Quantum tautology      91
Quasi topology      201
Random class      126
reality      4
Recursion      182
Recursive (group)      262
Recursively enumerable      190
Reduced (word)      261
Relativization (of a formula)      171
Representation      31
SAR      16 74
Self      16 73
Semantics      4
Semi-computable      178
Separable (ordering)      146
Set theory (Zermelo — Fraenkel)      44
SIMPLE      205
singular      148
Skolem's paradox      68
Special axioms (of L)      38
Standard interpretation      26
Standard model      7
Syntax      4 16
Tarski's theorem      79 240
Tautology      31 54
Term      6
text      3
Total function      203
Transfinite recursion      99
Truth function      26
Undefinability theorem      74
Variables      7
Versal      203
von Neumann theorem      82
Von Neumann universe      100
Well-ordering      96
Word identities (in groups)      184
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