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Journals and Conferences
We show that there exists a Turing degree which is minimal and fixed point free.
The strong weak truth table (sw) reducibility was suggested by Downey, Hirschfeldt, and LaForte as a measure of relative randomness, alternative to the Solovay reducibility. It also occurs naturally… (More)
We prove that every diagonally noncomputable function computes a set A which is bi-immune, meaning that neither A nor its complement has an infinite computably enumerable subset.
We show that the identity bounded Turing degrees of computably enumerable sets are not dense.
For any P ⊆ 2ω, define S(P), the degree spectrum of P, to be the set of all Turing degrees a such that there exists A ∈ P of degree a. We prove a number of basic properties of the structure which is… (More)
We say that A ≤LR B if every B-random number isA-random. Intuitively this means that if oracle A can identify some patterns on some real !, oracle B can also find patterns on !. In other words, B is… (More)
We show that there exists a real α such that, for all reals β, if α is linear reducible to β (α ≤` β, previously denoted α ≤sw β) then β ≤T α. In fact, every random real satisfies this… (More)
Lipschitz continuity is used as a tool for analyzing the relationship between incomputability and randomness. Having presented a simpler proof of one of the major results in this area—the theorem of… (More)
The Turing degree of a real measures the computational difficulty of producing its binary expansion. Since Turing degrees are tailsets, it follows from Kolmogorov’s 0-1 law that for any property… (More)