COUNTABLE MEETS IN COHERENT SPACES WITH APPLICATIONS TO THE CYCLIC SPECTRUM

This paper reviews the basic properties of coherent spaces, characterizes them, and proves a theorem about countable meets of open sets. A number of examples of coherent spaces are given, including the set of all congruences (equipped with the Zariski topology) of a model of a theory based on a set of partial operations. We also give two alternate proofs of the main theorem, one using a theorem of Isbell's and a second using an unpublished theorem of Makkai's. Finally, we apply these results to the Boolean cyclic spectrum and give some relevant examples.