Tarski’s axiom
Tarski proposed the following axiom for set theory^{}:
For every set $S$, there exists a set $U$ which enjoys the following properties:

•
$S$ is an element of $U$

•
For every element $X\in U$, every subset of $X$ is also an element of $U$.

•
For every element $X\in U$, the power set^{} of $X$ is also an element of $U$.

•
Every subset of $U$ whose cardinality is less than the cardinality of $U$ is an element of $U$.
This axiom implies the axiom of choice^{}. It also implies the existence of inaccessible cardinal^{} numbers.
Title  Tarski’s axiom 

Canonical name  TarskisAxiom 
Date of creation  20130322 15:37:25 
Last modified on  20130322 15:37:25 
Owner  rspuzio (6075) 
Last modified by  rspuzio (6075) 
Numerical id  5 
Author  rspuzio (6075) 
Entry type  Definition 
Classification  msc 03E30 