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II - Program Size, Halting Probabilities, Randomness, & Metamathematics

Published online by Cambridge University Press:  23 November 2009

Gregory. J. Chaitin
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Summary

Having done the bulk of the work necessary to encode the halting probability Ω as an exponential diophantine equation, we now turn to theory. In Chapter 5 we trace the evolution of the concepts of program-size complexity. In Chapter 6 we define these concepts formally and develop their basic properties. In Chapter 7 we study the notion of a random real and show that Ω is a random real. And in Chapter 8 we develop incompleteness theorems for random reals.

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Algorithmic Information Theory , pp. 91
Publisher: Cambridge University Press
Print publication year: 1987

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