Measurable cardinal

Set theory concept

In mathematics, a measurable cardinal is a certain kind of large cardinal number. In order to define the concept, one introduces a two-valued measure on a cardinal κ, or more generally on any set. For a cardinal κ, it can be described as a subdivision of all of its subsets into large and small sets such that κ itself is large, ∅ and all singletons {α} are small, complements of small sets are large and vice versa. The intersection of fewer than κ large sets is again large.

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