Tarski–Grothendieck set theory
System of mathematical set theory / From Wikipedia, the free encyclopedia
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Tarski–Grothendieck set theory (TG, named after mathematicians Alfred Tarski and Alexander Grothendieck) is an axiomatic set theory. It is a non-conservative extension of Zermelo–Fraenkel set theory (ZFC) and is distinguished from other axiomatic set theories by the inclusion of Tarski's axiom, which states that for each set there is a Grothendieck universe it belongs to (see below). Tarski's axiom implies the existence of inaccessible cardinals, providing a richer ontology than ZFC. For example, adding this axiom supports category theory.
The Mizar system and Metamath use Tarski–Grothendieck set theory for formal verification of proofs.