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The cofinality of an ordinal is the length of the shortest possible sequence leading up to it from below[citation needed]. For example, the cofinality of \(\omega2\) is \(\omega\) because of the sequence \(\omega,\omega+1,\omega+2,\omega+3,\cdots\).

The cofinality of any countable limit ordinal is ω[1]. The cofinality of any successor ordinal is 1[2]. The cofinality of 0 is 0.

Regular

An ordinal is called regular if its cofinality equals itself.

  1. P. Nadathur, To Infinity And Beyond (p.27) (accessed 2021-03-15)
  2. P. Nadathur, To Infinity And Beyond (p.27) (accessed 2021-03-15)
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