Willard H. Dow

Willard Thompson

Complexity theory has a profound influence on the field of cryptology. The time complexity of breaking a cipher system must be significant enough to thwart any adversary from succeeding. However, with the emergence of quantum computers an adversary may have no difficulty in breaking known cipher systems. If quantum computers would exist today new mechanisms for security would need to be built. ...

A Separable Non-remainder of H Alan Dow and Klaas

We prove that there is a compact separable continuum that (consistently) is not a remainder of the real line.

Alan Dow

One of the many gifts from Alan to Set-theoretic Topology is the use of elementarity. For a while this was even known as “Dow’s method of elementary submodels”. But Alan would be, was, and still is the first to protest that the Löwenheim-Skolem theorem predates him by a few decades. We have for the longest time been familiar with recursive constructions where often beforehand a sequence of situ...

Dow And

We prove that the following statement follows from the Open Colouring Axiom (OCA): if X is locally compact σ-compact but not compact and if itš Cech-Stone remainder X * is a continuous image of ω * then X is the union of ω and a compact set. It follows that the remainders of familiar spaces like the real line or the sum of countably many Cantor sets need not be continuous images of ω * .

Willard Burr Soper