= GCH preservation by a finite-function collapse
{c}
If the ground model satisfies the <Generalized continuum hypothesis>, a <finite-function collapse to countable size> of $\kappa$ preserves it. The old $\kappa^+$ becomes the new $\aleph_1$, and there are at most $2^\kappa=\kappa^+$ names for subsets of $\omega$. For every old cardinal $\lambda\geq\kappa^+$ there are at most $2^{\lambda\cdot\kappa}=2^\lambda=\lambda^+$ names for subsets of $\lambda$. <Cardinal preservation by chain-condition forcing> and <Cantor theorem> turn these upper bounds into the required equalities.
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