Axiom of Monotonicity
Using the explosive operators, it is possible to give a recursive definition for the transfinite cardinals of Cantor. Also, the operator can be used to represent the powerset of a set. Making use of the fact that the explosive operators are monotonically increasing functions of its arguments, we arrive at an axiom we call, the axiom of monotonicity. It is very easy to derive the Generalized Continuum Hypothesis (GCH) from this axiom. Since, Axiom of Choice (AC) follows from GCH, we have AC also as a theorem of Intuitive Set Theory (IST).