Statement of research interests:

I am especially active in that part of topology which is involved with set-theoretic consistency and independence of some very basic topological concepts. This is part of what I call the legacy of Kurt Goedel, who first showed that there are mathematical statements whose truth or falsity cannot be decided on the basis of the axioms on which all of mathematics up to Goedel's day was based. Although over sixty years have passed since then, no one has come up with any new axioms that are generally seen to be true. However, in the meantime, a multitude of statements in mathematics, including some in almost every one of the main areas of pure mathematics, have been shown to be undecidable on the basis of the generally accepted axioms. Many of them are easy to state, in fact easier to state and more fundamental to some branches of mathematics, than most of the true statements that are being proven in these branches today.

Topology is one branch that has been completely revolutionized in the past three decades as a result. Ever since 1977, I have been a leading researcher in the part of topology that deals with these consistency and independence results. To take just one example: in 1948, M. Katetov proved that a compact space is metrizable if, and only if, every subspace of its cube is normal; he then asked whether ``cube'' could be replaced by ``square''. In 1977, I showed that it is consistent that the answer is negative, while in 2001, P. Larson and S. Todorcevic showed that it is consistent that the answer is affirmative.

An expository article of mine on independence results has been recently published electronically in Topology Atlas.