\documentclass{article}

\newtheorem{theorem}{Theorem}

\begin{document}

\begin{theorem}
This is the main theorem.
\end{theorem}

\begin{theorem}[$c^\star$ case]
This is a sub-case of the main theorem.
\end{theorem}

\begin{theorem}[$w^\star$ case]
This is another sub-case of the main theorem.
\end{theorem}

\end{document}