A new aspect of the cozero lattice in pointfree topology

The cozero part Coz L of a frame L has been studied quite extensively, but invariably from the point of view that it is a sigma-frame - a fact proved with the aid of the Axiom of Countable Choice. Here, it will be shown that, for certain purposes the latter is not, required. For this a new description is presented of the realcompletion of a completely regular frame in terms of Coz L which does not involve any choice principle. The key to this is the introduction of a particular type of ideal in Coz L which amounts to a choice-free form of the sigma-ideals usually considered in this context. (C) 2009 Elsevier B.V. All rights reserved.