ELSEVIER zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA TOPOLOGY AND ITS APPLICATIONS Topology and its Applications 55 (1994) 185-194 Co-absolutes of U( w,) Alan Dow * zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO Department of Mathematics, York University, 4700 Keele Street, North York, Ont., Canada M3J IP3 Klaas Pieter Hart * * Faculty of Technical Mathematics and Informatics, TU Delft, Postbus 5031, 2600 GA Delft, Netherlands (Received 19 February 1992) (Revised 31 August 1992) zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONM Abstract Our main results are: (1) after adding any number of Cohen reals to a model of GCH the space U(o,> is co-absolute with a power of w2 and (2) there is a model in which U(o,) is not co-absolute with any product of discrete spaces. Key words: Uniform ultrafilter; U(wI); Density; Co-absolute; Cohen reals; Suslin trees AMS CMOS) Subj. CZuss.: Primary 06E0.5, 54D80; secondary 03E35 1. Introduction This paper deals with the density and co-absolutes of the space U(w,> of uniform ultrafilters on wl. Recall that in [2] Baumgartner showed that in every ccc extension of a model of 2”’ = w2 the cellularity of U(w,) is still w2. In [4] Miller shows that if K many Cohen reals, where K G 2”2, are added (to a model of 2”1 = 0,) then even the density of U(w,) is still w2 (Miller points out that the case K = w3 is due to Kunen). We remove Miller’s restriction on K by showing that if any number of Cohen reals are added to a model of 2”” = w2 the space U(o,) is co-absolute with a product of discrete spaces-just as in the Balcar-Vopgnka theorem. This allows us to conclude that the density of CJ(wl) is w2, because none of the factors can be larger than w2 and the number of factors can be at most 2”‘. * E-mail: dowa@nexus.yorku.ca. * * Corresponding author. E-mail: wiawkph@dutrun2.tudeIft.n1. 0166-8641/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved SSDI 0166-8641(93)E0041-L