The degree of disjunction, δ(F), of a family F of functions is the least cardinal Ï„ such that every pair of functions in F agree on a set of cardinality less than Ï„. Suppose θ, μ, λ, κ are non-zero cardinals with θ ≤ μ ≤ λ. This paper is concerned with functions which map μ-sized subsets of λ into κ. We first show there is always a ‘large’ family F of such functions satisfying δ(F) ≤ θ. Next we determine the cardinalities of families F of such functions that are maximal with respect to δ(F) ≤ θ
