to obtain a free copy of Acrobat Reader to view PDF files.)
Papers to appear
- The structure of locally compact normal spaces: some quasi-perfect preimages, in Topology and its Applications.
- Special ultrafilters and cofinal subsets of ${}^\w\w, <^*)$. to Archive for Mathematical Logic
- The uniform box product $\Pi_\mu$, in Topology Proceedings.
- Classic Problems III. in Topology and its Applications.
Papers submitted for publication
- The Normal Reed Space Problem and a related example. to Fundamenta Mathematicae.
- (with Lyubomyr Zdomskyy) Locally compact, $omega_1$-compact spaces. to Annals of Pure and Applied Logic
Papers in various stages of preparation
- The structure theory of T_5 and related locally compact, locally connected spaces under the PFA and PFA(S)[S],
- The fine structure of locally compact, hereditarily normal spaces under strong conditions I
- Frechet uniform box products
- A collectionwise normal, hereditarily weakly theta-refinable Dowker space
- Some screenable anti-Dowker spaces
- Uniform box powers and products
- Scales, topological reflections, and large cardinal issues
- Generalized Kurepa and MAD families and topology
- The Tukey order for graphs
- Closed 2-1 preimages of $\omega_1$ and coherent 2-coloring systems
- Discontinuities and smooth curves in n-space
- Antidiamond and anti-PFA axioms and topological applications
- Elbow room in normed vector spaces
- Moving-off collections and spaces of continuous functions
- A note on C_k(irrationals)
- The compact-open topology and its sequential modification: stratifiability and an application to theoretical computer science
- Diagonalizable and related spaces
- Updates on a 1903 theorem of G. H. Hardy
- Frayed octants: test spaces in the structure theory of locally compact spaces
Expository paper
It is a shame that expository writing in mathematics is so little valued today. This modest little paper is only one of a great many I would have done, were exposition even half so well rewarded as research.Hilbert's First and Second Problems and the foundations of mathematics
This article, recently published electronically by Topology Atlas, discusses two (actually, three - I briefly speak about Hilbert's tenth poblem) of the twenty-odd problems Hilbert delivered in a 1900 address at the International Congress of Mathematicians. It was the basis for a one-hour colloquium lecture I gave at the University of Auckland in May, 2000, just three months before the 100th anniversary of Hilbert's lecture.