Existence of a measurable cardinal $\kappa$ by the existance of $\kappa$-complete ultrafilter
137203
Measurable cardinal existence condition
23442
Cardinality of the union of infinite and countable sets
82236
Extension of the Lebesgue measurable sets
116146
A cardinal $\kappa$ such that $2^{\lambda}<\kappa$ for all $\lambda<\kappa$ is regular?
150605
Existence of a regular uncountable $\aleph_{\alpha}$ without $\mathsf{AC}$
140662
Powers of infinite cardinals in the generic extension
7007
If $\alpha$ is a regular cardinal, the union of an elementary chain of $\alpha$-saturated models is also a $\alpha$-saturated model
97557
supremum of uncountable families of Borel measurable functions
82778
If a measure is semifinite, then there are sets of arbitrarily large but finite measure
107160
Open Set and Measure Theory
25306
A countable family of point-wise bounded functions defined on finite measurable set is actually uniformly bounded on a closed subset
60424
Uncountable family of uncountable compact subsets of $\mathbb{R}$
53663
outer measure and measurable sets
139612
Follow-up regarding right-continuous $f:\mathbb{R} \to\mathbb{R}$ is Borel measurable
14496
Is there any example of a non-measurable set whose proof of existence doesn't appeal to the Axiom of choice?
156161
Banach-Tarski theorem without axiom of choice
41683
Pre-image of a measurable set A is always measurable?