Fodor's lemma

The set of Fodor (also: Pressing Down Lemma ) is a set of set theory, which was discovered in 1956 by the Hungarian mathematician Géza Fodor. He says that there are always large (ie, stationary ) subsets for certain functionality on which to accept this only one value.

Statement

Let be a stationary subset of a regular, uncountable cardinal number. Is a regressive function, that is, applies to everyone, so there is a stationary set on which is constant, ie there exists a so that applies to everyone.

Evidence

Assuming the statement is not true: Then for each, the amount would be non-stationary. Therefore, the complements of each club sets, that is, elements of the club filter. This is complete opposite diagonal sections, therefore applies. Since is stationary, is. But for true: and therefore for all. This is in contradiction to the regressivity. So the assumption is false, that is, there is such a stationary quantity.