8 problems

Let $x$ be an infinite set, let $\omega$ be the first infinite ordinal, and let $\mathcal P(\omega)$ denote the power set of $\omega$. Cantor's continuum hypothesis. There is no ca…

Let $\mathsf{CH}$ denote the continuum hypothesis, and let $\mathsf{ZFC}$ denote Zermelo–Fraenkel set theory with the axiom of choice. A statement is independent of $\mathsf{ZFC}$…

Let $C^2(\alpha9omega)$ denote the inner model obtained from second-order definability over $\alpha9omega$, let $\text{CH}$ denote the continuum hypothesis, and let $M_n$ denote th…

Brouwer's continuum hypothesis. Cantor's second number class and the continuum have the same number of points.

Let CH denote the continuum hypothesis. A statement is canonically necessary if it holds in every canonical model under the notions of canonicity developed in the paper. The conjec…

Let $\mathbf T$ be the semi-intuitionistic set theory described in the source, and let $\mathrm{CH}$ denote the continuum hypothesis: every infinite set of reals is either in one-t…

Let $X$ be a locally compact, non-compact, separable metrizable space, and let $X^*$ denote its Stone–Čech remainder. An autohomeomorphism of $X^*$ is a homeomorphism from $X^*$ to…

Let $x$ be a set with cardinality $\kappa$, let $\mathcal{P}(x)$ denote its powerset, and let $\kappa^+$ be the least cardinal greater than $\kappa$. Generalized Continuum Hypothes…