Maximal almost disjoint sets of transversals. Measurable Cardinals Probability measures. Under CH, Lebesgue measure cannot be extended onto all subsets of the reals. Real-valued measurable cardinals and measurable cardinals. These cardinals are inaccessible.
Measurable cardinals are weakly compact.
Measurable cardinals are Ramsey. Extendability of Lebesgue measure. Solovay's equiconsistency theorem for measurable and real-valued measurable cardinals. Elementary Submodels Submodels vs. elementary submodels. The Tarski-Vaught Criterion.