\begin{frame}{Recursive Languages}
  \begin{block}{}
    A language $L$ is \emph{recursive} if 
    \begin{itemize}\setlength{\itemsep}{0pt}
      \item $L$ is recursively enumerable, and
      \item $\overline{L}$ is recursively enumerable.
    \end{itemize}
  \end{block}
  \pause\medskip

  \begin{goal}{}
    Not every recursively enumerable language is recursive!
  \end{goal}
  (See the a few slides back.)
  \pause\bigskip

  \begin{goal}{Theorem}
    A language $L$ is recursive $\iff$ 
    $L$ is accepted by a deterministic TM $M$
    that reaches for every input a halting state.
  \end{goal}
  Proof on the next slide.
\end{frame}