We say that A ≤LR B if every B-random set is A-random with respect to Martin-Löf randomness. We study this reducibility and its interactions with the Turing reducibility, Π1 classes, hyperimmunity and other recursion theoretic notions. A natural variant of the Turing reducibility from the point of view of Martin-Löf randomness is the LR reducibility which was introduced in [12]. We say that A ≤...

The high/low hierarchy respects the ordering of degrees, and so we can expect to find properties of order which are possessed by all degrees in a given hierarchy class. Such properties can also be found for classes of the generalized high/low hierarchy even though that hierarchy does not respect the ordering of the degrees. For example, Jockusch and Posner [4], extending a result of Cooper [l],...

We show that over the base system P− + Σ2-bounding, the existence of a 1-generic degree < 0′′ bounding a minimal degree is equivalent to Σ2-induction.

In this work we characterize different types of solutions of a vector optimization problem by means of a scalarization procedure. Usually different scalarizing functions are used in order to obtain the various solutions of the vector problem. Here we consider different kinds of solutions of the same scalarized problem. Our results allow us to establish a parallelism between the solutions of the...

A computable structure A is x-computably categorical for some Turing degree x, if for every computable structure B ∼= A there is an isomorphism f : B → A with f ≤T x. A degree x is a degree of categoricity if there is a computable structure A such that A is x-computably categorical, and for all y, if A is y-computably categorical then x ≤T y. We construct a Σ2 set whose degree is not a degree o...

In this paper I recall the reasons in favour of extending the classical conception of truth to include degrees of truth as well as truth value gaps and gluts, then provide a sketch of a new system of logic that provides all of these simultaneously. Despite its power, the resulting system is quite simple, combining degrees of truth and degrees of falsity to provide a very flexible and elegant co...

d-Fenfluramine (d-Fen) has been demonstrated to alter body temperature (BT), decrease 5-hydroxytryptamine (5-HT) and decrease 5-HT plasma membrane transporters (PMT) in rats. Therefore, experiments were designed to test whether a correlation existed between elevated BT and brain 5-HT depletions. It was hypothesized that d-Fen would induce hyperthermia if the environmental temperature was elevat...

The local adsorption structure of methylthiolate in the ordered Au(111)-(sqrt[3]xsqrt[3])R30 degrees phase has been investigated using core-level-shift measurements of the surface and bulk components of the Au 4f(7/2) photoelectron binding energy. The amplitude ratio of the core-level-shift components associated with surface Au atoms that are, and are not, bonded to the thiolate is found to be ...