We construct two examples of a compact, 0-dimensional space which supports a Radon probability measure whose measure algebra is isomor-phic to the measure algebra of 2 ! 1. The rst construction uses } to produce an S-space with no convergent sequences in which every perfect set is a G. A space with these properties must be both hereditarily normal and hereditarily countably paracompact. The sec...

We use Prolog as a flexible meta-language to provide executable specifications of some fundamental mathematical objects and their transformations. In the process, isomorphisms are unraveled between natural numbers and combinatorial objects (rooted ordered trees representing hereditarily finite sequences and rooted ordered binary trees representing Gödel’s System T types). This paper focuses on ...

Using forcing we produce a model of ZFC + CH (with 2 arbitrarily large) and, in this model, we obtain a characterization of the Abelian groups G (necessarily of size at most 2) which admit: (i) a hereditarily separable group topology, (ii) a group topology making G into an S-space, (iii) a hereditarily separable group topology that is either precompact, or pseudocompact, or countably compact (a...