Here we are making use of the convention, introduced in Chapter 1, that TRUE=1,FALSE=0. Hence predicates are just total functions whose values are always either 0 or 1. And therefore, it makes perfect sense to say that some given predicate is or is not computable. Let P (x1, …, ...
it is almost equally easy to define and investigate computable functions of an integral variable or a real or computable variable, computable predicates, and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit trea...
computable atomic measure μ with the property that the initial segment complexity of each μ-random sequence dominates no computable function, and a computable atomic measure ν with the property that the initial segment complexity of each ν-random sequence is dominated by all computable functions....