Fixed-point lemma for normal functions: Difference between revisions

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== Background and formal statement ==

A [[normal function]] is a [[proper class|class]] function ''f'' from the class Ord of [[ordinal numbers]] to itself so that:

* ''f'' is '''strictly increasing''': ''f''(&alpha;) &le;< f(&beta;) whenever &alpha; &le;< &beta;.

* ''f'' is '''continuous''': for every limit ordinal &lambda;, ''f''(&lambda;) = sup { f(&alpha;) : &alpha; < &lambda; }.

It can be shown that if ''f'' is normal then ''f'' commutes with [[supremum|suprema]]; for any set ''A'' of ordinals,