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Franzén T. — G #246 del's Theorem: An Incomplete Guide to Its Use and Abuse
Franzén T. — G #246 del's Theorem: An Incomplete Guide to Its Use and Abuse

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Название: G #246 del's Theorem: An Incomplete Guide to Its Use and Abuse

Автор: Franzén T.

Аннотация:

The theorem is tossed about and misapplied by the uninformed, so the author gathered up quotes and responses he's been involved with on the internet and tackled a presentation for what he terms a "general audience." Mathematicians will turn to more sophisticated treatments; determined non-mathematicians with a strong bent for formal logic will be able to make their way through this explication. The author is a philosopher by training but has worked for a couple decades in computer science at the Swedish Institute of Computer Science and is affiliated with Lulea U. of Technology, Sweden.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2005

Количество страниц: 172

Добавлена в каталог: 29.11.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\omega$-consistency      3 22
$\Sigma$-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
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