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math.LO2016
A note on the differences of computably enumerable reals
George Barmpalias, Andrew Lewis-Pye
We show that given any non-computable left-c.e. real there exists a left-c.e. real such that for all left-c.e. reals and all right-c.e. reals . The proof is…
math.LO2016
Optimal asymptotic bounds on the oracle use in computations from Chaitin's Omega
George Barmpalias, Nan Fang, Andrew Lewis-Pye
Chaitin's number Omega is the halting probability of a universal prefix-free machine, and although it depends on the underlying enumeration of prefix-free machines, it is always Tu…