Past exam of the mathematics course of the University of Cambridge / 2013 / iii / Paper 19 / 2 / i / c

The singular cardinals hypothesis is the assertion that for every infinite singular cardinal $\kappa$,In particular, for a singular strong-limit cardinal it gives $2^{\kappa }={\kappa }^{+}$. This is a restriction on singular-cardinal exponentiation; it does not assert the full Generalized continuum hypothesis at all cardinals.