Bilaniuk S. — A Problem Course in Mathematical Logic (vol. 1) :: Электронная библиотека попечительского совета мехмата МГУ

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Bilaniuk S. — A Problem Course in Mathematical Logic (vol. 1)

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Название: A Problem Course in Mathematical Logic (vol. 1)

Автор: Bilaniuk S.

Аннотация:

This is a text for a problem-oriented undergraduate course in mathematical logic. It covers the basics of propositional
and first-order logic through the Soundness, Completeness, and Compactness Theorems. Volume II, Computation, covers the basics of computability using Turing machines and recursive functions, the Incompleteness Theorems, and complexity theory through the P and NP. Information on availabality and the conditions under which this book may be used and reproduced are given in the preface.

Язык:

Рубрика: Математика/Алгебра/Математическая логика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: Version 1.5

Год издания: 1999

Количество страниц: 89

Добавлена в каталог: 09.12.2004

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

Предметный указатель

      7 24
      7 24
      24 25
      7
      11
      53
      11
      24
      79
      79
$\backslash$       79
$\cap$       79
$\cup$       79
$\exists$       30
$\forall$       24 25 30
$\in$       79
$\leftrightarrow$       9 30
$\mathbb{N}$       80
$\mathbb{Q}$       80
$\mathbb{R}$       80
$\mathcal{L}$       24
$\mathcal{L}_1$       26
$\mathcal{L}_=$       26
$\mathcal{L}_F$       26
$\mathcal{L}_G$       51
$\mathcal{L}_N$       26
$\mathcal{L}_O$       26
$\mathcal{L}_P$       7
$\mathcal{L}_S$       26
$\mathcal{L}_{NT}$       25
$\mathcal{P}$       79
$\mathcal{S}$       10
$\mathfrak{M}$       33
$\mathfrak{N}$       33
$\mathrm{Th}$       39 45
$\neg$       7 24 25
$\nvDash$       14 36 37
$\overline{Y}$       79
$\prod$       79
$\subseteq$       79
$\times$       79
$\to$       7 24 25
$\varphi^x_t$       42
$\vDash$       14 35 37
$\vee$       9 30
$\wedge$       9 30
abbreviations      9 30
ALL      2
AND      2 9
ASSIGNMENT      34 35
Assignment extended      35
Assignment truth      11
Atomic formulas      7 27
Axiom      15 28 39
Axiom, logical      43
Axiom, schema      15 42
Axiom, schema A1      15 42
Axiom, schema A2      15 42
Axiom, schema A3      15 42
Axiom, schema A4      42
Axiom, schema A5      42
Axiom, schema A6      42
Axiom, schema A7      42
Axiom, schema A8      42
Bound      29
Bound variable      29
Chicken      80
CLIQUE      52
Compactness Theorem      20 50
Compactness Theorem, applications of      51
Complement      79
Completeness theorem      20 50 83
Connectives      7 9 24
Consistent      19 47
Consistent, maximally      19 48
Constant      24 25 31 33 35
Contradiction      13 38
Convention, common symbols      25
Convention, parentheses      9 30
Countable      80
Cross product      79
Deduction      16 43
Deduction Theorem      17 44 83
EDGE      52
Egg      80
Element      79
Elementary equivalence      54
Equality      24 25
Equivalence elementary      54
Existential quantifier      30
Extension of a language      30
finite      80
First-order languages      23
First-order logic      2 23
For all      25
Formula      7 27
Formula, atomic      7 27
Formula, unique readability      10 32
free      29
Free variable      29

Function      24 31 33 35
Function, -place      24 25
Generalization      42
Generalization Theorem      45 83
Generalization Theorem on Constants      45
Gothic characters      33
Graph      52
Greek characters      7 28 81
if ... then      2 7 25
If and only if      9
Implies      14 38
Inconsistent      19 47
Independent set      52
Inference rule      15
Infinite      80
Infinite Ramsey's Theorem      53
Infinitesimal      55
Intersection      79
Isomorphism of structures      53
john      80
Language      26 31
Language, extension of      30
Language, first-order      23
Language, formal      1
Language, natural      1
Language, propositional      7
Limericks      83
Logic, first-order      2 23
Logic, mathematical      1
Logic, natural deductive      1
Logic, predicate      7
Logic, propositional      2 7
Logic, sentential      7
Logical axiom      43
Maximally consistent      19 48
Metalanguage      31
Metatheorem      31
Model      37
modus ponens      15 43
MP      15 43
Natural deductive logic      1
Non-standard model      53 55
Non-standard model of the real numbers      55
NOT      2 7 25
OR      2 9
Parentheses      7 24
Parentheses, conventions      9 30
Parentheses, doing without      8
Power set      79
Predicate      24 25
Premiss      16 43
proof      16 43
Propositional logic      2 7
Proves      16 43
Punctuation      7 25
Quantifier, existential      30
Quantifier, scope of      30
Quantifier, universal      24 25 30
Ramsey number      53
Ramsey's theorem      53
Relation      24 31 33
Relation, -place      24 25 79
Relation, binary      25 80
Rule of inference      15 43
Satisfiable      13 37
Satisfies      13 36 37
Scope of a quantifier      30
Sentence      29
Sentential logic      7
Set theory      79
Soundness Theorem      19 47 83
Structure      33
Subformula      10 29
Subgraph      52
Subset      79
Substitutable      41
Substitution      41
symbols      7 24
Symbols, logical      24
Symbols, non-logical      24
Tautology      13 38
Term      26 31 35
Term, unique readability      32
Theorem      31
Theory      39 45
There is      2
Truth table      12 13
Truth values      11
Truth, in a structure      36 37
Uncountable      80
union      79
Unique readability of formulas      10 32
Unique readability of terms      32
Unique Readability Theorem      10 32
Universal quantifier      30
Universe      33
Variable      24 31 34 35
Vertex      52
witnesses      48
Word      80

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