More forcing and reflection in topology
by
Alan Dow
York University

We continue the study of the structure of compact spaces in the presence of countable restrictions on the convergence structure. Our experience leads to the view that the technique of iterated small forcings and reflection (model theoretic) is an integral part of the topic. We will defend this thesis (not that there are a lot of antagonists, thankfully) by illustrating its use in the proof of some recent theorems.

Theorem It is consistent that every compact separable radial space is Fréchet.

Theorem It is consistent to have the value of the continuum large and to have that compact sequential spaces are pseudoradial.

This last result is motivated by Sapirovski's CH result that compact sequential spaces are pseudoradial. It is a joint result with Juhasz, Soukup, and Szentmiklossy.

Date received: February 14, 1996

Copyright © 1996 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caab-80.