  Let $\epsilon, C$ be two positive real numbers, and $\mathcal C \subset
\mathbb R$ be a DCC (descending chain condition) set. Let $(X, B = \sum b_j
B_j)$ denote a projective surface with an $\mathbb R$-divisor. Then
  (1) The class $\{X\}$ of surfaces for which there exists a divisor $B$ such
that $(X,B)$ is $\epsilon$-log terminal and $-(K_X + B)$ is nef (excluding only
those for which at the same time $K_X\equiv 0$, $B=0$, and $X$ has at worst Du
Val singularities), is bounded.
  (2) The set $\{(K_X + B)^2\}$ of squares for the semi log canonical pairs
$(X, B)$ with ample $K_X + B$ and $b_j \in \mathcal C$, is a DCC set.
  (3) The class $\{(X,B)\}$ of pairs such that $(X, B)$ is semi log canonical,
$K_X + B$ is ample, $(K_X + B)^2 = C$ and $b_j \in \mathcal C$, is bounded.
