Countable meets in coherent spaces with applications to the cyclic spectrum

Michael Barr, John F. Kennison, and R. Raphael

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 We also give two alternate proofs of the main theorem, one using a theorem of Isbell's and a second using an unpublished theorem of Makkai's. Finally, we apply these results to the Boolean cyclic spectrum and give some relevant examples.

Keywords: countable localic meets of subspaces, Boolean flows, cyclic spectrum

2000 MSC: 06D22, 18B99, 37B99

Theory and Applications of Categories, Vol. 25, 2011, No. 19, pp 508-532.

Published 2011-11-19.

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