= One-Cohen-real preservation of GCH
{title2=$\mathrm{GCH}\text{ preserved by one Cohen real}$}
Over a <Generalized continuum hypothesis> ground model, adding one Cohen real preserves every infinite power $2^\lambda=\lambda^+$. For the countable <forcing>, nice <subset> <forcing names> for $\lambda$ number at most $(2^{\aleph_0})^\lambda=2^\lambda$ in the ground model. Old <subsets> give the matching lower bound and the <countable chain condition for forcing> preserves <cardinals>. Starting from the <constructible universe>, the new real is nonconstructible while the constructible levels remain unchanged.
Back to article page
