We prove various results on the notion of ordinal ultrafiters introduced by J. Baumgartner. In particular, we show that this notion of ultrafilter complexity is independent of the more familiar Rudin-Keisler ordering.

We prove the consistency of a singular cardinal λ with small value of the ultrafilter number uλ, and arbitrarily large value of 2 . 2000 Mathematics Subject Classification. 03E05, 03E55.

We show the consistency of statement: “the set of regular cardinals which are the character of some ultrafilter on ω is not convex”. We also deal with the set of π-characters of ultrafilters on ω.

We prove that every continuum of weight ℵ 1 is a continuous image of thě Cech-Stone-remainder R * of the real line. It follows that under CH the remainder of the half line [0, ∞) is universal among the continua of weight c — universal in the 'mapping onto' sense. We complement this result by showing that 1) under MA every continuum of weight less than c is a continuous image of R * , 2) in the ...

Let D be an ultrafilter on the set N of natural numbers. To each function p: N — N and each ultrafilter E that is mapped to D by p, we associate a Dedekind cut in the ultrapower ö-prod N. We characterize, in terms of rather simple closure conditions, the cuts obtainable in this manner when various restrictions are imposed on E and p. These results imply existence theorems, some known and some n...

Abstract Given a bounded convex subset C of Banach space X and free ultrafilter $${\mathcal {U}}$$ U , we study which points $$(x_i)_{\mathcal ( x i ) are extreme the ultrapower $$C_{\mathcal <mml...

For a quantale V, the category V-Top of V-valued topological spaces may be introduced as a full subcategory of those V-valued closure spaces whose closure operation preserves finite joins. In generalization of Barr’s characterization of topological spaces as the lax algebras of a lax extension of the ultrafilter monad from maps to relations of sets, for V completely distributive, V-topological ...

‎for a given measure space $(x,{mathscr b},mu)$ we construct all measure spaces $(y,{mathscr c},lambda)$ in which $(x,{mathscr b},mu)$ is embeddable‎. ‎the construction is modeled on the ultrafilter construction of the stone--v{c}ech compactification of a completely regular topological space‎. ‎under certain conditions the construction simplifies‎. ‎examples are given when this simplification o...