Fodor's lemma

In mathematics, particularly in set theory, Fodor's lemma states the following: If

is a regular, uncountable cardinal,

is a stationary subset of

f ( α ) = γ

α ∈

In modern parlance, the nonstationary ideal is normal.

The lemma was first proved by the Hungarian set theorist, Géza Fodor in 1956.

It is sometimes also called "The Pressing Down Lemma".

If Fodor's lemma is false, for every

α < κ

there is some club set

α

α

α < κ

The club sets are closed under diagonal intersection, so

β < α

β < α

Fodor's lemma also holds for Thomas Jech's notion of stationary sets as well as for the general notion of stationary set.

Another related statement, also known as Fodor's lemma (or Pressing-Down-lemma), is the following: For every non-special tree

and regressive mapping

, with respect to the order on

), there is a non-special subtree

This article incorporates material from Fodor's lemma on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License.