Date of Award
Doctor of Philosophy (PhD)
We first use some results of Menas to prove that every normal filter on PKλ extends the cub filter on PKλ thereby settling a basic question in the structure theory of filters on PKλ.
Then we investigate ideal-theoretic and other aspects of ineffability properties of PKλ with particular emphasis on those which can be viewed as PKλ generalizations of weak compactness.
In the course of these studies, we came to view mild λ-ineffability as a PKλ generalization of weak compactness in an ideal-theoretically weak sense, and sought a PKλ generalization of weak compactness in an ideal-theoretically stronger sense.
To this end, we define the λ-Shelah property, a new ineffability property of PKλ between mild λ-ineffability and almost λ-ineffability, and prove results which support the contention that this is the property we sought.
These results include characterizations of the λ-Shelah property in terms of a normal ideal on PKλ and if λ K.
Carr, Donna Marie, "Ineffability Properties of Pkλ" (1981). Open Access Dissertations and Theses. Paper 3895.