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Families of partial functions
Published online by Cambridge University Press: 17 April 2009
Abstract
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The degree of disjunction, δ(F), of a family F of functions is the least cardinal τ such that every pair of functions in F agree on a set of cardinality less than τ.
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.
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- Copyright © Australian Mathematical Society 1983
References
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