\begin{frame}{Incompleteness Theorem}
  \begin{goal}{}
    We consider the sets of function and predicate symbols:
    \begin{scenter}
      $\asetfuncs = \setexp{\const{0},\, \sunfunc{S}, \sbinfunc{+}, \,\sbinfunc{\cdot}} $
        \hspace*{3ex}
      $\asetpreds = \setexp{ \sbinpred{<} }$
    \end{scenter}\pause{}
    with as intended model \emph{number theory $\boldsymbol{\standardN}$}:
    \begin{itemize}\setlength{\itemsep}{0pt}
      \item domain of $\standardN$ is $\nat$, the natural numbers (with 0)
    \pause
      \item
        $\intin{\const{0}}{\standardN} = 0$
    \pause
      \item
        $\intin{\sunfunc{S}}{\standardN}(n) = n+1$
    \pause
      \item
        $\intin{\sbinfunc{+}}{\standardN}(n,m) = n+m$
    \pause
      \item   
        $\intin{\sbinfunc{\cdot}}{\standardN}(n,m)  = n\cdot m$
    \pause
      \item 
        $\intin{\sbinpred{<}}{\standardN} = \descsetexp{\pair{n}{m}}{n,m\in\nat \text{ such that } n