Homework Implementation: Covering the Bases

Covering all the bases.

Covering all the bases in academic medicine.

S1 Like all of my predecessors, I have spent a substantial amount of time during my year as President reviewing the addresses delivered by my extraordinarily distinguished predecessors and wondering how I could possibly say anything new, different, or in any way memorable. Like my more recent predecessors, my concerns about the quality of my Presidential Address were either compounded by, or pe...

Covering all bases: design and implementation of case analysis for contextual objects

We consider the question: Does a set of patterns cover all objects of a given type? This is straightforward in the simply-typed setting, but undecidable in the presence of dependent types. We discuss the question in the setting of Beluga, a dependently-typed programming and reasoning environment which supports programming with contextual objects and contexts. We describe the design and implemen...

Nice Hamel bases under the Covering Property Axiom

In the paper we prove that axiom CPA prism, which follows from the Covering Property Axiom CPA and holds in the iterated perfect set model, implies that there exists a Hamel basis which is a union of less than continuum many pairwise disjoint perfect sets. We will also give two consequences of this last fact. 1 The result and its consequences In this paper we will use standard set theoretic ter...

Algebras with Positive Bases, Commutators and Covering Numbers

We describe how a general setup called "Algebras with positive bases" can be used for a concurrent study of conjugacy-class covering numbers and character covering numbers in …nite groups. This approach yields improvements on the known bounds of the covering numbers.