\documentclass{rtaloop}
\rtalabel{fixed-point}

\begin{document}
\begin{solvedproblem}{Richard Statman}{}{June 1993}

\begin{abstract}
Is there a fixed point combinator $Y$ for which $Y \leftrightarrow^* Y(SI)$?
\end{abstract}

It has been remarked by C. B\"ohm \cite{B84:nh} that $Y$ is a fixed point
combinator if and only if $Y
\leftrightarrow^* (SI)Y$ ($Y$ and $SIY$ are convertible). Also, if $Y$ is a
fixed point combinator, then so is $Y(SI)$.  Is there is a
fixed point combinator $Y$ for which $Y \leftrightarrow^* Y(SI)$?

\begin{remark}
This was solved by Benedetto Intrigila \cite{Intrigila:IC97}
who showed that there is no such fixed point combinator.
\end{remark}

\end{solvedproblem}
\end{document}