New posts in Set Theory

Is there an object such that its unique existence follows from choice axiom, while its existence cannot be proven without choice axiom?

Foundations without axiom schema of replacement

Finding, for each $\alpha < \omega_1$, an ordinal $\beta > \alpha$ such that $L_{\beta + 1} \models \beta \text{ is countable}$

Why doesn't the fact we can force the continuum hypothesis outright prove the continuum hypothesis?

Does the independence of the axiom of choice imply Gödel's incompleteness theorem?

Without Foundation, can axiom of choice be derived from $\forall\alpha\in\mathbf{Ord} (P(\alpha)\text{ can be well ordered})$?

Proper Subgroup of $O_2(\mathbb{R})$ Isomorphic to $O_2(\mathbb{R})$

How can someone reject a math result if everything has to be proved?

Is Fodor's Lemma necessary for the $\omega_1$ train station puzzle?

Does the collection of all $0$-$1$ random variables form a set?