Definition:Cofinality
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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
Sources
- 1971: Gaisi Takeuti and Wilson M. Zaring: Introduction to Axiomatic Set Theory: $\S 10.61$