Zermelo set theory
Noun
Meaning
Zermelo set theory
(set theory) An early and influential axiomatisation of set theory.
Examples
Indeed, Zermelo set theory already can interpret second-order arithmetic and much of type theory in finite types, which in turn are sufficient to formalize the bulk of mathematics.
The system of PM is roughly comparable in strength with Zermelo set theory (or more precisely a version of it where the axiom of separation has all quantifiers bounded).