Published online by Cambridge University Press: 01 December 2016
Assuming AD, we show that all of the ordinals below $\delta _5^1$ represented by descriptions (c.f. [2], but also defined below) are cardinals. Using this analysis we also get a simple representation for the cardinal structure below
$\delta _5^1$. As an application, we compute the cofinalitites of all cardinals below
$\delta _5^1$.