In mathematical logic, a cardinal number κ such that for every function f: κ < ω → {0, 1} there is a set of cardinality κ that is homogeneous for f, is called a Ramsey cardinal.
Note: κ < ω is the set of all finite subsets of κ.
A cardinal κ is almost Ramsey iff for every function f: κ < ω → {0, 1} and for every λ < κ, there is a set of order type λ that is homogeneous for f.