Definition:Cofinality

Formal Definition
Let $\kappa$ be an ordinal.

The cofinality of $\kappa$, denoted $\map {\mathrm {cf} } \kappa$, is the smallest ordinal $\lambda$ such that:


 * $\map {\mathrm {cof} } {\kappa, \lambda}$

where $\map {\mathrm {cof} } {\kappa, \lambda}$ denotes the cofinal relation.

Intuitive Definition
Cofinality describes the smallest ordinal capable of reaching $\kappa$ "from below" using some mapping.

Also see

 * Definition:Regular Cardinal
 * Definition:Singular Cardinal