Information-theoretic Incompleteness

Information-theoretic Incompleteness (1992)

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by G.J. Chaitin

Venue:	APPLIED MATHEMATICS AND COMPUTATION
Citations:	7 - 1 self

BibTeX

@ARTICLE{Chaitin92information-theoreticincompleteness,
    author = {G.J. Chaitin},
    title = {Information-theoretic Incompleteness},
    journal = {APPLIED MATHEMATICS AND COMPUTATION},
    year = {1992}
}

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Abstract

We propose an improved definition of the complexity of a formal axiomatic system: this is now taken to be the minimum size of a selfdelimiting program for enumerating the set of theorems of the formal system. Using this new definition, we show (a) that no formal system of complexity n can exhibit a specific object with complexity greater than n + c, and (b) that a formal system of complexity n can determine at most n + c scattered bits of the halting probability\Omega . We also present a short, self-contained proof of (b).

Citations

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264	Algorithmic Information Theory - Chaitin - 1987
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