A set A ⊆ ω is called 2-computably enumerable (2-c.e.), if there are computably enumerable sets A1 and A2 such that A1 −A2 = A. A set A ⊆ ω is quasi-reducible to a set B ⊆ ω (A ≤Q B), if there is a computable function g such that for all x ∈ ω we have x ∈ A if and only if Wg(x) ⊆ B. This reducibility was introduced by Tennenbaum (see [1], p.207) as an example of a reducibility which differs fro...

The study of the free idempotent generated semigroup IG(E) over a biordered set E began with the seminal work of Nambooripad in the 1970s and has seen a recent revival with a number of new approaches, both geometric and combinatorial. Here we study IG(E) in the case E is the biordered set of a wreath product G ≀ Tn, where G is a group and Tn is the full transformation monoid on n elements. This...

A recent debate has focused on different methodological principles underlying the practice of axiom choice in mathematics (cf. Feferman et al., 2000; Maddy, 1997; Easwaran, 2008). The general aim of these contributions can be described as twofold: first to clarify the spectrum of informal justification strategies retraceable in the history of mathematical axiomatics. Second, to evaluate and to ...