Erdos cardinal

In mathematics, an Erdős cardinal is a certain kind of large cardinal number.

Formally, a cardinal number κ which is the least cardinal such that for every function f: κ ^{< ω} → {0, 1} there is a set of order type α that is homogeneous for f, is called an α-Erdős cardinal. Existence of zero sharp implies that the constructible universe L satisfies "for every countable ordinal α, there is an α-Erdős cardinal". However, existence of an ω₁-Erdős cardinal implies existence of zero sharp.