New Axioms for Set Theory . Axiom schema: If ZFC proves that for all measurable cardinals κ, φ holds in the .. cardinals; in fact, ground models for forcing usually satisfy GCH.
Arthur W. Apter . Mathematical Logic, specifically Set Theory: Large Cardinals and Forcing. "On the Class of Measurable Cardinals Without the Axiom of Choice", ..
Topics in Discovering Modern Set Theory. II. . Real-valued measurable cardinals and measurable cardinals. These cardinals are inaccessible. Measurable cardinals are weakly compact.
[math/9808012] The Lottery Preparation . the forcing to shoot a club C in kappa which avoids the measurable cardinals and the forcing to add various long Prikry sequences.
