Fixed-point lemma for normal functions: Difference between revisions

Revision as of 20:32, 5 October 2007

Revision as of 20:33, 5 October 2007

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The fixed point lemma states that the class of fixed points of any normal function is nonempty and in fact is unbounded: given any ordinal α, there exists an ordinal β such that β ≥ α and ''f''(β) = β.

The continuity of the normal function implies the setclass of fixed points is closed (the supremum of any subset of the class of fixed points is again a fixed point). Thus the fixed point lemma is equivalent to the statement that the fixed points of a normal function form a [[club set|closed and unbounded]] class.

== Proof ==