Some points in β<i>N</i>

Abstract

Abstract Assuming either the continuum hypothesis or Martin's axiom, we show that in the space β N – N , there are: ( a ) points which are not P -points, but which are also not limit points of any countable set, and ( b ) a countable set of points dense in itself such that each of the points is not a limit point of any countable discrete set. Our method is to construct such points in the Stone space of a measure algebra, and then embed that Stone space into β N – N . We also, by a similar use of measures, establish the independence of the existence of selective ultrafilters by showing that there are none in the random real model.