  We show that assuming modest large cardinals, there is a definable class of
ordinals, closed and unbounded beneath every uncountable cardinal, so that for
any closed and unbounded subclasses $P, Q$, $\langle L[P],\in ,P \rangle$ and
$\langle L[Q],\in ,Q \rangle$ possess the same reals, satisfy the Generalised
Continuum Hypothesis, and moreover are elementarily equivalent. The theory of
such models is thus invariant under set forcing. They also all have a rich
structure satisfying many of the usual combinatorial principles and a definable
wellorder of the reals. One outcome is that we can characterize the inner model
constructed using definability in the language augmented by the H\"artig
quantifier when such a $P$ is itself $Card$.
