\begin{frame}{Definability Results for Reachability/Unreachability}
  \begin{proposition}
    Let $\sbinpred{R}$ be a binary relation symbol.
    
    \begin{enumerate}\setlength{\itemsep}{0.6ex}
    \pause
      \item 
        In predicate logic, 
        \emph{reachability} by $\sbinpred{R}$-steps is: 
        \pause
        \begin{itemize}\vspace*{0.4ex}\setlength{\itemsep}{0.4ex}
          \item \alert{not definable} by a sentence.
          \item \alert{not definable} by a set of sentences. 
        \end{itemize}
        \vspace*{0.75ex}
    \pause
      \item 
        In predicate logic, 
        \emph{unreachability} by $\sbinpred{R}$-steps is: 
        \pause
        \begin{itemize}\vspace*{0.4ex}\setlength{\itemsep}{0.4ex}
          \item \alert{not definable} by a single sentence.
          \item \emph{definable} by a set of sentences.
        \end{itemize}
    \end{enumerate}
  \end{proposition}
  \pause
    
  \begin{proof}
    Similar to definability and undefinability results (see earlier)
    for finiteness and infiniteness.
  \end{proof}    
\end{frame}