Skip to main content
Log in

Algorithmic Information Theory and Undecidability

  • Published:
Synthese Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  • Chaitin, Gregory J.: 1974a, 'Information-Theoretic Computational Complexity', IEEE Transactions on Information Theory IT-20, pp. 10–15.

  • Chaitin, Gregory J.: 1974b, 'Information-Theoretic Limitations of Formal Systems', Journal of the ACM 21, 403–424.

    Google Scholar 

  • Chaitin, Gregory J.: 1975a, 'Randomness and Mathematical Proof', Scientific American 232(5), 47–52.

    Google Scholar 

  • Chaitin, Gregory J.: 1975b, 'A Theory of Program Size Formally Identical to Information Theory', Journal of the ACM 22, 329–340.

    Google Scholar 

  • Chaitin, Gregory J.: 1986, 'Randomness and Gödel's Theorem', Mondes en Developpement, 54-55, 125–128.

    Google Scholar 

  • Chaitin, Gregory J.: 1987a, 'Incompleteness Theorem for Random Reals', Advances in Applied Mathematics 8, 119–146.

    Google Scholar 

  • Chaitin, Gregory J.: 1987b, Algorithmic Information Theory, Cambridge University Press, Cambridge.

    Google Scholar 

  • Chaitin, Gregory J.: 1988, 'Randomness in Arithmetic', Scientific American 259(1), 80–85.

    Google Scholar 

  • 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.

  • Chaitin, Gregory J.: 1990, 'A Random Walk in Arithmetic', New Scientists 24, 44–46.

    Google Scholar 

  • Chaitin, Gregory J.: 1992, 'Information-Theoretic Incompleteness', Applied Mathematics and Computation 52, 83–101.

    Google Scholar 

  • 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. Reprinted in G. Chaitin: The Limits of Mathematics, Springer, Singapore, 1998, pp. 1-27.

  • Delahaye, Jean-Paul: 1989, 'Chaitin's Equation: an Extension of Gödel's Theorem', Notices of the A.M.S. 36(8), 984–987.

    Google Scholar 

  • Gardner, Martin: 1979, 'Mathematical Games: the Random Number Omega Bids Fair to Hold the Mysteries of the Universe', Scientific American 241(5), 20–43.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

  • Kreisel, Georg: 1980, 'Kurt Gödel', Biographical Memoirs of Fellows of the Royal Society 26, 149–224.

    Google Scholar 

  • Kreisel, Georg and Azriel Levy: 1968, 'Reflection Principles and their Uses for Establishing the Complexity of Axiomatic Systems', Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 14, 97–142.

    Google Scholar 

  • Li, Ming and Paul Vitanyi: 1993, An Introduction to Kolmogorov Complexity and its Applications, Springer-Verlag, New York.

    Google Scholar 

  • van Lambalgen, Michiel: 1989, 'Algorithmic Information Theory', Journal of Symbolic Logic 54, 1389–1400.

    Google Scholar 

  • Mostowski, Andrzej: 1952, Sentences Undecidable in Formalized Arithmetic - An Exposition of the Theory of Kurt Gödel, North-Holland, Amsterdam.

    Google Scholar 

  • Odifreddi, Piergiorio: 1989, Classical Recursion Theory, North-Holland, Amsterdam.

    Google Scholar 

  • 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.

    Google Scholar 

  • Post, Emil: 1948, 'Degrees of Recursive Unsolvability', Bulletin of the A.M.S. 54, 641–42.

    Google Scholar 

  • Putnam, Hilary: 1965, 'Trial and Error Predicates and the Solution to a Problem of Mostowski', Journal of Symbolic Logic 30, 49–57.

    Google Scholar 

  • Raatikainen, Panu: 1998, 'On Interpreting Chaitin's Incompleteness Theorem', Journal of Philosophical Logic 27, 569–86.

    Google Scholar 

  • Rogers, Hartley Jr.: 1967, Theory of Recursive Functions and Effective Computability, McGraw-Hill, New York.

    Google Scholar 

  • Rosser, J. Barkley: 1937, 'Gödel's Theorems for Non-Constructive Logics', Journal of Symbolic Logic 2, 129–137.

    Google Scholar 

  • Stewart, Ian: 1988, 'The Ultimate in Undecidability', Nature 332, 115–16.

    Google Scholar 

  • 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.

    Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Raatikainen, P. Algorithmic Information Theory and Undecidability. Synthese 123, 217–225 (2000). https://doi.org/10.1023/A:1005298819345

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1005298819345

Keywords

Navigation