New posts in Cardinals

In ZF, if injection from A to B doesn't exist, then does surjection from A to B exist?

Rank $ (a) {\aleph_4}^{\aleph_4}, (b) {\aleph_0}^{\aleph_4}, (c) {\aleph_4}^{\aleph_0}, (d) {\aleph_4}, (e) {\aleph_5}, (f) {\aleph_5}^{\aleph_0} $

Can there be numbers with $ℵ_n$ digits?(n>0)

Degree of a field extension by a transcendental element

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

Why does the number of possible probability distributions have the cardinality of the continuum?

Manifold that's not $\aleph_1$-separable

Assuming the falsity of continuum hypothesis is added as an axiom, how do we produce sets with cardinality in-between $\Bbb N$ and $\Bbb R$?

Do any proofs/properties rely on the distinction between some uncountable size and a larger uncountable size, in order for the proof/property to hold?

Given $\lambda$ regular cardinal, $\left(\kappa^{<\lambda}\right)^{<\lambda}=\kappa^{<\lambda}$?