The Rudin-Balogh Technique
by
Chris Good
University of Birmingham

Over the past few years, Zoltan Balogh has solved a number of significant open problems using a refined version of a technique perhaps first used by Mary Ellen Rudin to construct a normal, but not collectionwise normal, space of cardinality c, the continuum, in ZFC. Most notably Balogh constructs an hereditarily normal Dowker space of size c in ZFC. The technique can be seen as a ZFC-\diamondsuit construction: c many countable elementary submodels on c predict enough behaviour on small fragments of the space to define the required topology. The price paid for constructing these examples in ZFC is that they typically have large character.

In this talk we hope to give a good idea of how to put the Rudin-Balogh technique into practice by looking at one of Balogh's constructions, without worrying too much about the technicalities of the set-theory that makes it work.

Date received: September 7, 2000