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Answer by Lorenzo for Consistency of a strange (choice-wise) set of reals

Here is another way to show the consistency of such a set by a direct symmetric extension approach:Let $\mathbb{P}$ be the forcing that add Cohen reals (by reals I mean elements of $\omega^\omega$)...

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Answer by Elliot Glazer for 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}:...

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

Consider a set $X\subseteq \mathbb{R}$ such that$X$ is not separable wrt its subspace topologyFor all $r\in\mathbb{R}$ there exists a sequence $(x_n)_{n\in\omega} \subset X$ converging to $r$In a model...

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