In mathematical set theory, an Ulam matrix is an array of subsets of a cardinal number with certain properties. Ulam matrices were introduced by Stanislaw Ulam in his 1930 work on measurable cardinals: they may be used, for example, to show that a real-valued measurable cardinal is weakly inaccessible.
Definition Suppose that and are cardinal numbers, and let be a -complete filter on . An Ulam matrix is a collection of subsets of indexed by such that If then and are disjoint. For each , the union over of the sets , is in the filter .
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