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Results tagged with selection-principles
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user 6794
5
votes
Accepted
Reference request: The consistency of a tall tower in $\mathbb{N}^\mathbb{N}$
A theorem of Hechler says that, given any poset in which every countable subset has a strict upper bound, you can arrange for that poset to be cofinal in the $\leq^*$ ordering of $\mathbb N^{\mathbb N …
3
votes
Accepted
P-filter property?
After the clarifications in comments of OP (August 28 and today), here's a counterexample. Let $\mathcal F$ be the filter consisting of only $\omega-\{0\}$ and $\omega$. Then $\mathcal S$ (as defined …
21
votes
Accepted
Two strengthenings of "strong measure zero"
Strategically strong measure zero is equivalent to countable. To prove the nontrivial direction, suppose $X$ is strategically strong measure zero and $s$ is a winning strategy for player II. Consider …