\begin{frame}
  \frametitle{Examples}

  \begin{alertblock}{}
  Give a counter-model for:
  \begin{talign}
    &\myall{x}{\myex{y}{ R(x,y)}}, \\ 
    &\myall{x}{\myall{y}{\myall{z}{\big(R(x,y) \wedge R(y,z) \to R(x,z)\big)}}} \\
    &\quad \models\;\; \myex{x}{R(x,x)}
  \end{talign}
  \end{alertblock}  
  \bigskip
  
  So, what could be an infinite counter-model?
  \pause
  \begin{exampleblock}{}
    A counter-model:
    \begin{itemize}
      \item $A = \nat$ (the universe is the set of natural numbers)
      \item $R = {<}$ 
    \end{itemize}  
  \end{exampleblock}
  \vspace{10cm}
\end{frame}