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Term in mathematical set theory
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.[1]
Definition
Suppose that κ and λ 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
.
References