Table of Contents - 4. TG (TARSKI-GROTHENDIECK) SET THEORY

Here we introduce Tarski-Grothendieck (TG) set theory, named after
mathematicians Alfred Tarski and Alexander Grothendieck. TG theory extends
ZFC with the TG Axiom ax-groth, which states that for every set
there is an inaccessible cardinal such that is not in .
The addition of this axiom to ZFC set theory provides a framework for
category theory, thus for all practical purposes giving us a complete
foundation for "all of mathematics."

We first introduce the concept of inaccessibles, including weakly and
strongly inaccessible cardinals (df-wina and df-ina respectively ),
Tarski classes (df-tsk), and Grothendieck universes (df-gru). We
then introduce the Tarski's axiom ax-groth and prove various properties
from that.