  We prove preservation theorems for $\mathcal{L}_{\omega_1, G}$, the countable
fragment of Vaught's closed game logic. These are direct generalizations of the
theorems of \L{}o\'s-Tarski (resp. Lyndon) on sentences of
$\mathcal{L}_{\omega_1, \omega}$ preserved by substructures (resp. homomorphic
images). The solution, in $ZFC$, only uses general features and can be extended
to several variants of other strong first-order logic that do not satisfy the
interpolation theorem; instead, the results on infinitary definability are
used. This solves an open problem dating back to 1977. Another consequence of
our approach is the equivalence of the Vop\v{e}nka principle and a general
definability theorem on subsets preserved by homomorphisms.
