INFORMATION-THEORETIC INCOMPLETENESS Applied Mathematics and Computation

@inproceedings{Chaitin1992INFORMATIONTHEORETICIA,
  title={INFORMATION-THEORETIC INCOMPLETENESS Applied Mathematics and Computation},
  author={Gregory J. Chaitin},
  year={1992}
}
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 Ω. We also present a short, self… CONTINUE READING