# another definition of cofinality

Let $\kappa $ be a limit ordinal^{} (e.g. a cardinal). The cofinality of $\kappa $ $\mathrm{cf}(\kappa )$ could also be defined as:

$$\mathrm{cf}(\kappa )=inf\{|U|:U\subseteq \kappa \text{such that}supU=\kappa \}$$ |

($supU$ is calculated using the natural order of the ordinals^{}).
The cofinality of a cardinal is always a regular cardinal and hence $\mathrm{cf}(\kappa )=\mathrm{cf}(\mathrm{cf}(\kappa ))$.

This definition is equivalent^{} 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 |