another definition of cofinality

Let κ be a limit ordinalMathworldPlanetmath (e.g. a cardinal). The cofinality of κ cf(κ) could also be defined as:

cf(κ)=inf{|U|:Uκ such that supU=κ}

(supU is calculated using the natural order of the ordinalsMathworldPlanetmathPlanetmath). The cofinality of a cardinal is always a regular cardinal and hence cf(κ)=cf(cf(κ)).

This definition is equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmath to the parent definition.

Title another definition of cofinality
Canonical name AnotherDefinitionOfCofinality
Date of creation 2013-03-22 13:52:59
Last modified on 2013-03-22 13:52:59
Owner x_bas (2940)
Last modified by x_bas (2940)
Numerical id 9
Author x_bas (2940)
Entry type Definition
Classification msc 03E04