  The concepts of closed unbounded (club) and stationary sets are generalised
to $\gamma$-club and $\gamma$-stationary sets, which are closely related to
stationary reflection. We use these notions to define generalisations of
Jensen's combinatorial principles {$\Box$} and $\diamondsuit$.
  We define $\Pi^1_\gamma$-indescribability and use the new
$\Box^{\gamma}$-sequences to extend the result of Jensen that in the
constructible universe a regular cardinal is stationary reflecting if and only
if it is $\Pi^1_1$-indescribable: we show that in $L$ a cardinal is
$\Pi^{1}_{\gamma} $-indescribable iff it reflects $\gamma$-stationary sets.
More particularly (stating only the special case of $n$ finite):
  Theorem $(V=L)$ Let $n<\omega$ and $\kappa$ be $\Pi^{1}_{n}$-indescribable
but not $\Pi^1_{n+1}$-indescribable, and let $A\subseteq\kappa$ be
$n+1$-stationary. Then there are $E_{A}\subseteq A$ and a $\Box^{n}$-sequence
$S$ on $\kappa$ such that $E_{A}$ is $n+1$-stationary in $\kappa$ and $S$
avoids $E_{A}$. Thus $\kappa$ is not $n+1$-reflecting.
  Certain assumptions on the $\gamma$-club filter allow us to prove that
$\gamma$-stationarity is downwards absolute to $L$, and allows for splitting of
$\gamma$-stationary sets. We define $\gamma$-ineffability, and look into the
relation between $\gamma$-ineffability and various $\diamondsuit$ principles;
we show that $\gamma$-ineffability is downward absolute to $L$.
