Tarski’s axiom

Tarski proposed the following axiom for set theoryMathworldPlanetmath:

For every set S, there exists a set U which enjoys the following properties:

  • S is an element of U

  • For every element XU, every subset of X is also an element of U.

  • For every element XU, the power setMathworldPlanetmath 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 choiceMathworldPlanetmath. It also implies the existence of inaccessible cardinalMathworldPlanetmath numbers.

Title Tarski’s axiom
Canonical name TarskisAxiom
Date of creation 2013-03-22 15:37:25
Last modified on 2013-03-22 15:37:25
Owner rspuzio (6075)
Last modified by rspuzio (6075)
Numerical id 5
Author rspuzio (6075)
Entry type Definition
Classification msc 03E30