The computable Lipschitz reducibility was introduced by Downey, Hirschfeldt and LaForte under the name of strong weak truthtable reducibility [6]. This reducibility measures both the relative randomness and the relative computational power of real numbers. This paper proves that the computable Lipschitz degrees of computably enumerable sets are not dense. An immediate corollary is that the Solo...

We introduce a notion of relative primeness for equivalence relations, strengthening the non-reducibility, and show many standard benchmark relations that non-reducibility may be strengthened to primeness. several analogues cardinal properties Borel including prime relation partition on quotient spaces. In particular, we weak compactness, characterize ${\mathbb F}_2$ E}_1$. also discuss dichoto...

We show that polynomial time truth-table reducibility via Boolean circuits to SAT is the same as log space truth-table reducibility via Boolean formulas to SAT and the same as log space Turing reducibility to SAT. In addition, we prove that a constant number of rounds of parallel queries to SAT is equivalent to one round of parallel queries. Finally, we show that the infinite difference hierarc...

In the early 1980s, Selman’s seminal work on positive Turing reductions showed that positive Turing reduction to NP yields no greater computational power than NP itself. Thus, positive Turing and Turing reducibility to NP differ sharply unless the polynomial hierarchy collapses. We show that the situation is quite different for DP, the next level of the boolean hierarchy. In particular, positiv...

We show that every basis for the countable Borel equivalence relations strictly above E0 under measure reducibility is uncountable, thereby ruling out natural generalizations of the Glimm-Effros dichotomy. We also push many known results concerning the abstract structure of the measure reducibility hierarchy to its base, using arguments substantially simpler than those previously employed.

This article expands our work in (LNCS 9709 (2016), 225–233). By its reliance on Turing computability, the classical theory of effectivity, along with effective reducibility and Weihrauch reducibility, is only applicable to objects that are either countable or can be encoded by objects. We propose a notion effectivity based Koepke’s Ordinal Machines (OTMs) applies arbitrary set-theoretical Π 2 ...

In this paper we study reducibility of those representations of quasi-split unitary p-adic groups which are parabolically induced from supercuspidal representations of general linear groups. For a supercuspidal representation associated via Howe’s construction to an admissible character, we show that in many cases a criterion of Goldberg for reducibility of the induced representation reduces to...

We study weak 2 randomness, weak randomness relative to ∅′ and Schnorr randomness relative to ∅′. One major theme is characterizing the oracles A such that ML[A] ⊆ C, where C is a randomness notion and ML[A] denotes the Martin-Löf random reals relative to A. We discuss the connections with LR-reducibility and also study the reducibility associated with weak 2randomness.

4 Programming in system F 17 4.1 Free structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 4.2 Representing free structures in system F . . . . . . . . . . . . . . 19 4.3 The case of integers: representable functions . . . . . . . . . . . . 22 4.4 Towards normalization: the reducibility technique . . . . . . . . 23 4.5 Reducibility and polymorphism . . . . . . . . . . . . . . ....

an extensive study of fischer-tropsch synthesis (fts) on alumina-supported cobalt catalysts promoted with different amounts of ruthenium and rhenium is reported. up to 2 wt% of promoters, are added to the catalyst by coimpregnation. the catalysts are characterized by different methods including: bet physisorption, x-ray diffraction, hydrogen chemisorption, and temperature-programmed reduction. ...