The Singular Cardinals Hypothesis (SCH) is a statement in set theory, a branch of mathematical logic that deals with sets, their properties, and relationships. It specifically deals with the behavior of cardinal numbers, which are used to measure the size of sets.
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The singular cardinals hypothesis asserts that every infinite singular cardinal satisfiesEquivalently, for every infinite singular cardinal. Here is the gimel function. The Generalized continuum hypothesis implies this principle, but the principle only constrains the indicated singular-cardinal exponentiation.