Information-Theoretic Limitations of Formal Systems

@article{Chaitin1974InformationTheoreticLO,
  title={Information-Theoretic Limitations of Formal Systems},
  author={Gregory J. Chaitin},
  journal={J. ACM},
  year={1974},
  volume={21},
  pages={403-424}
}
  • G. Chaitin
  • Published 1 July 1974
  • Computer Science
  • J. ACM
An attempt is made to apply information-theoretic computational complexity to meta-mathematics. The paper studies the number of bits of instructions that must be given to a computer for it to perform finite and infinite tasks, and also the time it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theorems from the… 
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  • 1974
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This paper reviews algorithmic information theory, which is an attempt to apply information-theoretic and probabilistic ideas to recursive function theory. Typical concerns in this approach are, for
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A subset of information theory as it applies to computer science is presented, which aims to comprehensively present a branch of mathematics that attempts to quantify information.
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Gödel's theorem may be demonstrated using arguments having an informationtheoretic flavor. In such an approach it is possible to argue that if a theorem contains more information than a given set of
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TLDR
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  • Computer Science
    [1988] Proceedings. Structure in Complexity Theory Third Annual Conference
  • 1988
The authors provide an introduction to the main ideas of Kolmogorov complexity and survey the wealth of useful applications of this notion. It is based on a theory of information content of strings,
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  • 1974
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A definition of the degree of randomness of individual binary strings is led to and an information-theoretic version of Godel's theorem on the limitations of the axiomatic method is examined.
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