-
2
-
-
0016082450
-
Information-Theoretic Limitations of Formal Systems
-
Chaitin, Gregory J.: 1974b, 'Information-Theoretic Limitations of Formal Systems', Journal of the ACM 21, 403-424.
-
(1974)
Journal of the ACM
, vol.21
, pp. 403-424
-
-
Chaitin, G.J.1
-
3
-
-
0002034420
-
Randomness and Mathematical Proof
-
Chaitin, Gregory J.: 1975a, 'Randomness and Mathematical Proof, Scientific American 232(5), 47-52.
-
(1975)
Scientific American
, vol.232
, Issue.5
, pp. 47-52
-
-
Chaitin, G.J.1
-
4
-
-
0016532771
-
A Theory of Program Size Formally Identical to Information Theory
-
Chaitin, Gregory J.: 1975b, 'A Theory of Program Size Formally Identical to Information Theory', Journal of the ACM 22, 329-340.
-
(1975)
Journal of the ACM
, vol.22
, pp. 329-340
-
-
Chaitin, G.J.1
-
5
-
-
33748189295
-
Randomness and Gödel's Theorem
-
Chaitin, Gregory J.: 1986, 'Randomness and Gödel's Theorem', Mondes en Developpement, 54-55, 125-128.
-
(1986)
Mondes en Developpement
, vol.54-55
, pp. 125-128
-
-
Chaitin, G.J.1
-
6
-
-
0000761947
-
Incompleteness Theorem for Random Reals
-
Chaitin, Gregory J.: 1987a, 'Incompleteness Theorem for Random Reals', Advances in Applied Mathematics 8, 119-146.
-
(1987)
Advances in Applied Mathematics
, vol.8
, pp. 119-146
-
-
Chaitin, G.J.1
-
8
-
-
0008718848
-
Randomness in Arithmetic
-
Chaitin, Gregory J.: 1988, 'Randomness in Arithmetic', Scientific American 259(1), 80-85.
-
(1988)
Scientific American
, vol.259
, Issue.1
, pp. 80-85
-
-
Chaitin, G.J.1
-
9
-
-
3843112036
-
Undecidability and Randomness in Pure Mathematics
-
(a transcript of a lecture delivered 28 September 1989 at SOLVAY conference in Brussels) published in G. J. Chaitin: World Scientific
-
Chaitin, Gregory J.: 1989, 'Undecidability and Randomness in Pure Mathematics', (a transcript of a lecture delivered 28 September 1989 at SOLVAY conference in Brussels) published in G. J. Chaitin: Information, Randomness & Incompleteness, 2nd edn., World Scientific, 1990, pp. 307-313.
-
(1989)
Information, Randomness & Incompleteness, 2nd Edn.
, pp. 307-313
-
-
Chaitin, G.J.1
-
10
-
-
0038122178
-
A Random Walk in Arithmetic
-
Chaitin, Gregory J.: 1990, 'A Random Walk in Arithmetic', New Scientists 24, 44-46.
-
(1990)
New Scientists
, vol.24
, pp. 44-46
-
-
Chaitin, G.J.1
-
12
-
-
12444256873
-
Randomness in Arithmetic and the Decline and Fall of Reductionism in Pure Mathematics
-
Chaitin, Gregory J.: 1993, 'Randomness in Arithmetic and the Decline and Fall of Reductionism in Pure Mathematics', EATCS Bulletin, No. 50 (June 1993), pp. 314-328.
-
(1993)
EATCS Bulletin, No. 50 (June 1993)
, pp. 314-328
-
-
Chaitin, G.J.1
-
13
-
-
0004287895
-
-
Reprinted Springer, Singapore
-
Reprinted in G. Chaitin: The Limits of Mathematics, Springer, Singapore, 1998, pp. 1-27.
-
(1998)
The Limits of Mathematics
, pp. 1-27
-
-
Chaitin, G.1
-
14
-
-
33748205856
-
Chaitin's Equation: An Extension of Gödel's Theorem
-
Delahaye, Jean-Paul: 1989, 'Chaitin's Equation: an Extension of Gödel's Theorem', Notices of the A.M.S. 36(8), 984-987.
-
(1989)
Notices of the A.M.S.
, vol.36
, Issue.8
, pp. 984-987
-
-
Delahaye, J.-P.1
-
15
-
-
0009228180
-
Mathematical Games: The Random Number Omega Bids Fair to Hold the Mysteries of the Universe
-
Gardner, Martin: 1979, 'Mathematical Games: the Random Number Omega Bids Fair to Hold the Mysteries of the Universe', Scientific American 241(5), 20-43.
-
(1979)
Scientific American
, vol.241
, Issue.5
, pp. 20-43
-
-
Gardner, M.1
-
16
-
-
0011286239
-
-
Harrington, L. A., M. D. Morley, A. Scederov and S. G. Simpson (eds): North-Holland, Amsterdam
-
Harrington, L. A., M. D. Morley, A. Scederov and S. G. Simpson (eds): 1985, Harvey Friedman's Research on the Foundations of Mathematics, North-Holland, Amsterdam.
-
(1985)
Harvey Friedman's Research on the Foundations of Mathematics
-
-
-
17
-
-
33746803442
-
Introductory Note to 1930b, 1931 and 1932b
-
S. Feferman et al. (eds), Kurt Gödel: Oxford University Press, 1986
-
Kleene, Stephen C.: 1986, 'Introductory Note to 1930b, 1931 and 1932b', in S. Feferman et al. (eds), Kurt Gödel: Collected Works, Vol. 1, Oxford University Press, 1986, pp. 126-141.
-
(1986)
Collected Works, Vol. 1
, vol.1
, pp. 126-141
-
-
Kleene, S.C.1
-
21
-
-
0000528936
-
Algorithmic Information Theory
-
van Lambalgen, Michiel: 1989, 'Algorithmic Information Theory', Journal of Symbolic Logic 54, 1389-1400.
-
(1989)
Journal of Symbolic Logic
, vol.54
, pp. 1389-1400
-
-
Van Lambalgen, M.1
-
24
-
-
0041484427
-
A Mathematical Incompleteness in Peano Arithmetic
-
J. Barwise (ed.), North-Holland, Amsterdam
-
Paris, Jeff and Leo Harrington: 1977, 'A Mathematical Incompleteness in Peano Arithmetic', in J. Barwise (ed.), Handbook of Mathematical Logic, North-Holland, Amsterdam, pp. 1133-1142.
-
(1977)
Handbook of Mathematical Logic
, pp. 1133-1142
-
-
Paris, J.1
Harrington, L.2
-
25
-
-
0039934772
-
Degrees of Recursive Unsolvability
-
Post, Emil: 1948, 'Degrees of Recursive Unsolvability', Bulletin of the A.M.S. 54, 641-42.
-
(1948)
Bulletin of the A.M.S.
, vol.54
, pp. 641-642
-
-
Post, E.1
-
26
-
-
0002019785
-
Trial and Error Predicates and the Solution to a Problem of Mostowski
-
Putnam, Hilary: 1965, 'Trial and Error Predicates and the Solution to a Problem of Mostowski', Journal of Symbolic Logic 30, 49-57.
-
(1965)
Journal of Symbolic Logic
, vol.30
, pp. 49-57
-
-
Putnam, H.1
-
27
-
-
54649084125
-
On Interpreting Chaitin's Incompleteness Theorem
-
Raatikainen, Panu: 1998, 'On Interpreting Chaitin's Incompleteness Theorem', Journal of Philosophical Logic 27, 569-86.
-
(1998)
Journal of Philosophical Logic
, vol.27
, pp. 569-586
-
-
Raatikainen, P.1
-
29
-
-
23944446999
-
Gödel's Theorems for Non-Constructive Logics
-
Rosser, J. Barkley: 1937, 'Gödel's Theorems for Non-Constructive Logics', Journal of Symbolic Logic 2, 129-137.
-
(1937)
Journal of Symbolic Logic
, vol.2
, pp. 129-137
-
-
Rosser, J.B.1
-
30
-
-
0040913777
-
The Ultimate in Undecidability
-
Stewart, Ian: 1988, 'The Ultimate in Undecidability', Nature 332, 115-16.
-
(1988)
Nature
, vol.332
, pp. 115-116
-
-
Stewart, I.1
-
31
-
-
0011609067
-
The Concept of Truth in Formalized Languages
-
edited and translated by J. H. Woodger, Oxford University Press, Oxford
-
Tarski, Alfred: 1933/1956, 'The Concept of Truth in Formalized Languages', in Logic, Semantics, Metamathematics, edited and translated by J. H. Woodger, Oxford University Press, Oxford.
-
(1933)
Logic, Semantics, Metamathematics
-
-
Tarski, A.1
|