Measurable cardinal

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, $\emptyset$ and all singletons ${α}, α \in κ$ are small, complements of small sets are large and vice versa. The intersection of fewer than $κ$ large sets is again large.

单词	Measurable cardinal
释义	Measurable cardinal 英语百科 Measurable cardinal 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, $\emptyset$ and all singletons ${α}, α \in κ$ 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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