 Singular cardinals hypothesis

The singular cardinals hypothesis asserts that every infinite singular cardinal $\kappa$ satisfiesEquivalently, $\gimel (\kappa )=\max \{{\kappa }^{+},2^{\mathrm{cf}(\kappa )}\}$ for every infinite singular cardinal. Here $\gimel$ is the gimel function. The Generalized continuum hypothesis implies this principle, but the principle only constrains the indicated singular-cardinal exponentiation.

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.