Normality of X × ω1

Games of Length Ω1

We prove determinacy for open length ω1 games. Going further we introduce, and prove determinacy for, a stronger class of games of length ω1, with payoff conditions involving the entire run, the club filter on ω1, and a sequence of ω1 disjoint stationary subsets of ω1. The determinacy proofs use an iterable model with a class of indiscernible Woodin cardinals, and we show that the games precise...

The X Control Chart under Non-Normality

This paper studies design schemes for the X control chart under non-normality. Different estimators of the standard deviation are considered and the effect of the estimator on the performance of the control chart under non-normality is investigated. Two situations are distinguished. In the first situation, the effect of non-normality on the X control chart is investigated by using the control l...

Determinacy from Strong Compactness of Ω1

In the absence of the Axiom of Choice, the “small” cardinal ω1 can exhibit properties more usually associated with large cardinals, such as strong compactness and supercompactness. For a local version of strong compactness, we say that ω1 is Xstrongly compact (where X is any set) if there is a fine, countably complete measure on ℘ω1(X). Working in ZF + DC, we prove that the ℘(ω1)-strong compact...

Locally Compact, Ω1-compact Spaces

This paper is centered on an extremely general problem: Problem. Is it consistent (perhaps modulo large cardinals) that a locally compact space X must be the union of countably many ω-bounded subspaces if every closed discrete subspace of X is countable [in other words, if X is ω1-compact]? A space is ω-bounded if every countable subset has compact closure. This is a strengthening of countable ...

σ-Normality of Topological Spaces