Let $Card$ be the class of infinite cardinals and $p\colon Card^2\to Card$ be given by $(\kappa,\lambda)\mapsto\kappa^\lambda$. Assuming GCH it is known that $p(\kappa,\lambda)$ is …

This is not my area but a question occurred to me that I can not find the answer to. There is a very strong axiom of constructibility which ironically gives us highly non-construct …

While working on a project in operator algebras with a collaborator (and fellow MO user), we are able to successfully complete a transfinite induction assuming that the following h …

I assume ZFC. Let $U$ a set with the following (1), (2), (3): 1) $\omega\in U$ 2) $x\in U\ \Rightarrow x\subset U$ 3) $x\in U\ \Rightarrow \mathcal{P}(x)\in U$ (where $\mathc …

Let [J]: Jech "Set theory" (Millenium edition) Let $\kappa$ a limit ordinal. From [J], T.3.11, p. 33 we have that $\kappa<\kappa^{cf(\kappa)}$. I improved that proof, and ob …

The cardinal equation $\kappa^{\aleph_0}=2^\kappa$ is satisfied by $\kappa=\aleph_0$. It is also satisfied by any $\kappa$ for which $MA(\kappa)$ holds. Under $GCH$, the equati …