#
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unpublished theorem of Makkai's. Finally, we apply these results to the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.

http://www.tac.mta.ca/tac/volumes/25/19/25-19.dvi

http://www.tac.mta.ca/tac/volumes/25/19/25-19.ps

http://www.tac.mta.ca/tac/volumes/25/19/25-19.pdf

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/25/19/25-19.dvi

ftp://ftp.tac.mta.ca/pub/tac/html/volumes/25/19/25-19.ps

TAC Home