|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Franzén T. — G #246 del's Theorem: An Incomplete Guide to Its Use and Abuse |
|
|
|
| Предметный указатель |
 -consistency 3 22
 -soundness 22
ACA 109
Algorithm 12 64
Arithmetical component 22
Arithmetically sound 108
Arithmetization of syntax 35
Automatic theorem proving 72
Axiom 16 18
Axiom of constructibility 150
Axiomatic method 17
Axioms of infinity 57 150
Bernays, P. 98
Berry's paradox 142
Bishop, E. 82
Boolos, G. 143
Bounded formula 160
Bricmont, J. 2
Cantor, G. 70
Catalan's Conjecture 11
Chaitin's incompleteness theorem 139
Chaitin, G. 7
Chebyshev's theorem 148
Church, A. 68
Cohen, P. 34 150
Collatz conjecture 11
Complete theory 18 25
Completeness Theorem for first-order logic 5 26 127
complexity 23 137
Compressible string 138
Computable property 12 19
Computable set 64
Computably decidable 64
Computably enumerable 62
Conjecture, Catalan's 11
Conjecture, Collatz 11
Conjecture, Goldbach's 9
Conjecture, twin prime 10
Consistency 21
Consistency of PA 37 53 109
Consistency of ZFC 53
Consistency, proofs 37 107
Consistent theory 18
Continuum Hypothesis 34
Debray, R. 2
Decidable formal system 73
Diagonalization argument 69
Dialectica interpretation 5 39
Diophantine equation 10 71
Dirichlet's theorem 112
Dyson, F. 87
Edwards, J. 79
Einstein, A. 5
Elementary arithmetic 9
Elementary proof 15
Erdoes, P. 148
Essentially undecidable 75
Euclid 17
Euclidean geometry 17 51 127
Existential quantifier 155
exponentiation 156
Feferman, S. 100
Fermat's last theorem 1 11 15 111
Fermat, P. 15
Finitistic reasoning 39 106
Finsler, P. 6
First incompleteness theorem 3 16 74 157
First-order predicate language 128
First-order theory 17
Forcing 150
Formal language 16
Formal system 72 78
Frege, G. 98 128
Friedman, H. 33 153
Garrod, R. 23
Gentzen's consistency proof 38
Gentzen, G. 38 107
Godel, K., life and work 4
Godel, K., views on theology 90
Goedel numbering 35 49 66
Goedel sentence 42 55 84
Goedel's proof 40 48
Going outside the system 126
Goldbach's conjecture 9 12 161
Goldbach-like statement 12 21 160 162
Graves, D. 92
Halting problem 68
Hawking, S. 87
Henkin sentence 102
Henkin, L. 101
Hilbert's problems 15 34 70
Hilbert's program 39 106
Hilbert, D. 15 98 106
Hofstadter, D. 124
Human thought 80
Humanly provable statements 82
In principle 13
Incompleteness Theorem, First 3 16 74 157
Incompleteness Theorem, Second 3 34 98
Incompressible string 138
Induction axioms 132
Inexhaustibility 56 112 121
Inference rules 16
Infinite elements 135
Infinite regress 38
Institute for Advanced Study 5
Integers 10
Internet 1
Interpretation 130
Kadvany, J. 37
Kolmogorov complexity 57
Kripke, S. 47
Language of elementary arithmetic 9 155
| Leibniz, G.W. 136
Lexicographic ordering 62
Liar sentence 44
Ljunggren, W. 11
Lloyd, S. 89
Loeb's theorem 101
Logical consequence 130
Lucas, J.R. 55 117
Mihailescu, P. 11
Model 130
Model of a theory 51
Mohammed, N. 94
Morgenstern, O. 91
MRDP (Matiyasevich — Robinson — Davis — Putnam) theorem 31 46 54 70
Natural numbers 9
Negation 18
Negation complete 18
Newton, I. 136
Non ignorabimus 16 34
Nonstandard analysis 136
Nonstandard models 47 53 135
Numbers, integers 10
Numbers, irrational 25
Numbers, natural 9
Numbers, rational 25
Numbers, real 25
Numerical string 60
Occurrence of symbol in a string 60
omega 145
P (system) 3
PA 17 49 131
Paradox of the Liar 44 86
Parallel postulate 51
Paris — Harrington Theorem 56 152
Peano arithmetic 17
Penrose, R. 119
PM (Principia Mathematica) 2
Post, E. 6 70
Postmodernism 2 23 50
Presburger arithmetic 133
Presburger, M. 133
Prime 9
Programming language 68
Proof by mathematical induction 20
Proof in a formal system 16
Proof of consistency 37
Proof, elementary 15
Provable fixpoint 41
Quine, W.V.O. 42
Ramsey's theorem 152
Ramsey, F.P. 152
Rand, A. 78
Real numbers 25
Recursive unsolvability 68
Recursively enumerable 68
Relative consistency 107
Ribet, K.A. 15
Robinson arithmetic 48 160
Robinson, A. 136
Robinson, R.M. 160
Rosser sentence 43
Rosser, J.B. 3
Rucker, R. 115
Rules of reasoning 16
Russell, B. 2 98
Second incompleteness theorem 3 34 98
Second-order language 26
Self-reference 42 44
Sentence 18 28
Serres, M. 2
Simple set 70 142
Skepticism 103
Skolem, T. 6
Sokal, A. 2
Soundness properties 21
Soundness Theorem 130
String 59
Syntactic 28
Tarski's theorem 43
Tarski, A. 128
Theorem in a formal system 16
Theorem of Pythagoras 1 11
Theorem, Chebyshev's 148
Theorem, completeness 5
Theorem, completeness theorem 127
Theorem, Dirichlet's 112
Theorem, Fermat's 1 11 15
Theorem, Loeb's 101
Theorem, Matiyasevich — Robinson — Davis — Putnam (MRDP) 31 70
Theorem, Paris — Harrington 56 152
Theorem, Ramsey's 152
Theorem, soundness 130
Theorem, Tarski's 43
Theorem, undecidability 67
Theorem, unprovable 33
Theory 17
True arithmetical statement 30 31
True in the system 32
Truth 30
Turing machine 63
Turing, A. 6 63
Twin Prime Conjecture 10
Undecidability theorem 67
Undecidable sentence 18
Undecidable set 64
Universal quantifier 155
Unprovable truths 24
von Neumann, J. 97
Whitehead, A.N. 2 98
Wiles, A. 1 15
Zen Buddhism 4
Zermelo — Praenkel set theory 17
Zermelo, E. 3
ZFC 17 24 34 49 54 149
|
|
|
| Реклама |
|
|
|
|
|
О проекте