Information-Theoretic Limitations of Formal Systems

Authors:
Gregory J. Chaitin
Affiliations:
Rivadavia 3580, Depto. 10A, Buenos Aires, Argentina
Venue:
Journal of the ACM (JACM)
Year:
1974

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Abstract

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 axioms.