All Questions

Let X be an infinite set. Is it possible to show the existence of a countably infinite subset of X without using the Axiom of Choice?

I'm currently working on some universal algebra using proper classes (in MK class theory), and I repeatedly run into situations where I want to collect together some proper classes as the members of a ...

For any model of $M$ of ZFC, we can extend it to a model $M_{ew}$ with an "externally well-founded" predicate $ew$. For $x \in M$, We say that $M_{ew} \vDash ew(x)$ when there is no infinite ...

Suppose we start with a model $\mathcal{M}$ of $ZFC$ (or $GBC$ or $MK$ if you prefer), and let $N_0^\mathcal{M}$ denote the surreals in $\mathcal{M}$. If we add some large cardinal assumptions $\{\...