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13 votes
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Consistency of a strange (choice-wise) set of reals

The existence of such a set follows from $``\mathbb{R}$ is a countable union of countable sets.$"$ Let $\mathbb{R} = \bigcup_{n<\omega} S_n,$ each $S_n$ countable. Let $T_n = \{x \in \mathbb{R}: \exis …
Elliot Glazer's user avatar
4 votes
Accepted

Strong form of $\mathtt{PSP}$ for $K_\sigma$ sets

Here's a counterexample. Let $X$ be the set of bounded sequences, and let $A$ be the set of sequences which have only finitely many nonzero terms and achieve a strict maximum at the last nonzero term. …
Elliot Glazer's user avatar