  There have been many generalizations of Shoenfield's Theorem on the
absoluteness of $\Sigma^1_2$ sentences between uncountable transitive models of
$\mathrm{ZFC}$. One of the strongest versions currently known deals with
$\Sigma^2_1$ absoluteness conditioned on $\mathrm{CH}$. For a variety of
reasons, from the study of inner models and from simply combinatorial set
theory, the question of whether conditional $\Sigma^2_2$ absoluteness is
possible at all, and if so, what large cardinal assumptions are involved and
what sentence(s) might play the role of $\mathrm{CH}$, are fundamental
questions. This article investigates the possiblities for $\Sigma^2_2$
absoluteness by extending the connections between determinacy hypotheses and
absoluteness hypotheses.
