Zermelo–Fraenkel set theory, with the axiom of choice, commonly abbreviated ZFC, is the standard form of axiomatic set theory and as such is the most common foundation of mathematics.
Reference:
http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory
Reference:
http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory