On the Algorithmic Probability of Sets
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The combined universal probability m(D) of strings x in sets D is close to max (x) over x in D: their logs differ by at most D's information I(D:H) about the halting sequence H. As a result of this, given a binary predicate P, the length of the smallest program that computes a complete extension of P is less than the size of the domain of P plus the amount of information that P has with the halting sequence.
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