\begin{frame}[t]{(Un)Definability Results: Overview} \begin{goal}{} \medskip \begin{center} \begin{tabular}{|c|c|c|} \hline \multirow{2}{*}{\emph{property}} & \emph{definable} & \emph{definable} \\[-0.25ex] & \emph{by a sentence} & \emph{by a set of sentences} \\ \hline \hline \multirow{2}{*}{at least} & \multirow{2}{*}{$\checkmark$} & \multirow{2}{*}{$\checkmark$} \\[-0.5ex] & & \\ \hline \multirow{2}{*}{at most} & \multirow{2}{*}{$\checkmark$} & \multirow{2}{*}{$\checkmark$} \\[-0.5ex] & & \\ \hline \multirow{2}{*}{finiteness} & \multirow{2}{*}{$\xmark$} & \multirow{2}{*}{$\xmark$} \\[-0.5ex] & & \\ \hline \multirow{2}{*}{infiniteness} & \multirow{2}{*}{$\xmark$} & \multirow{2}{*}{$\checkmark$} \\[-0.5ex] & & \\ \hline \multirow{2}{*}{reachability} & \multirow{2}{*}{$\xmark$} & \multirow{2}{*}{$\xmark$} \\[-0.5ex] & & \\ \hline \multirow{2}{*}{unreachability} & \multirow{2}{*}{$\xmark$} & \multirow{2}{*}{$\checkmark$} \\[-0.5ex] & & \\ \hline % \end{tabular} \end{center} \medskip \end{goal} \end{frame}