Some more Problems about Orderings of Ultrafilters

Details Some more Problems about Orderings of Ultrafilters Some more Problems about Orderings of Ultrafilters

2010-05-14

arxiv.org/abs/1005.2590v1

Mathematics

Logic

7 pages

Scientific paper

We discuss the connection between various orders on the class of all the ultrafilters and certain compactness properties of abstract logics and of topological spaces. We present a model theoretical characterization of Comfort order. We introduce a new order motivated by considerations in abstract model theory. For each of the above orders, we show that if $E$ is a $(\lambda, \lambda)$-regular ultrafilter, and $D$ is not $(\lambda, \lambda)$-regular, then $E \not \leq D$. Many problems are stated.

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