This is a contribution to the study of the Muchnik and Medvedev lattices of non-empty Î 1 subsets of 2 Ï‰. In both these lattices, any non-minimum element can be split, i.e. it is the non-trivial joinâ€¦ (More)

Dobrinen and Simpson [4] introduced the notions of almost everywhere domination and uniform almost everywhere domination to study recursion theoretic analogues of results in set theory concerningâ€¦ (More)

An infinite binary sequence is complex if the Kolmogorov complexity of its initial segments is bounded below by a computable function. We prove that a Î 01 class P contains a complex element if andâ€¦ (More)

Let Pw and PM be the countable distributive lattices of Muchnik and Medvedev degrees of non-empty Î 1 subsets of 2 , under Muchnik and Medvedev reducibility, respectively. We show that all countableâ€¦ (More)

Blood pressure (BP) measurements obtained using 3 indirect BP measuring instruments, a Doppler ultrasonic flowmeter, an oscillometric device, and a photoplethysmograph, were compared with directâ€¦ (More)

We consider two axioms of second-order arithmetic. These axioms assert, in two different ways, that infinite but narrow binary trees always have infinite paths. We show that both axioms are strictlyâ€¦ (More)

The property of smallness for Î 1 classes is introduced and is investigated with respect to Medvedev and Muchnik degree. It is shown that the property of containing a small Î 1 class depends only onâ€¦ (More)

We continue the investigation of the path-connected geometry on the Cantor space and the related notions of dilution and compressibility described in [1]. These ideas are closely related to theâ€¦ (More)