If the longest constraint needs to be flushed to the right margin, you could use a tabular*
environment with two centered columns; something along these lines (change the lengths according to your needs):
\documentclass[reqno]{amsart}
\usepackage{array}
\newlength\MyIndent
\setlength\MyIndent{10em}
\begin{document}
\vspace{\abovedisplayskip}
\noindent\begin{tabular*}{\textwidth}{@{\hspace{\MyIndent}}>{$}c<{$}@{\extracolsep{\fill}}
>{$}c<{$}@{}}
a^2 + b^2 = ab & (a \in \{z,y,x,w,v,u\},\ b \neq 0) \\
a + b = c & (a \in \{z,y\},\ b = 0) \\
\end{tabular*}\par
\vspace{\belowdisplayskip}
\end{document}
If the longest constraint doesn't need to be flushed to the right margin, a simple array environment will do the job (change the lengths according to your needs):
\documentclass[reqno]{amsart}
\begin{document}
\[
\begin{array}{@{\hspace{7em}}c@{\hspace{3em}}c}
a^2 + b^2 = ab & (a \in \{z,y,x,w,v,u\},\ b \neq 0) \\
a + b = c & (a \in \{z,y\},\ b = 0) \\
\end{array}
\]
\end{document}
In order to fix that, you will have to give the \left\{
its counterpart which would be \right.
on the same line. The second line would need a \left. ... \right\}
.
As you do not need auto-sized brackets here, I would leave it all away.
Here is your example and my version:
% arara: pdflatex
\documentclass{article}
\usepackage{mathtools}
\begin{document}
\begin{align}
R = \left\{(S_1,S_1), (S_1,S_4), (S_4,S_4), (S_4,S_1), (S_2,S_2), (S_2,S_3), (S_3,S_3), (S_3,S_2), (S_0,S_0),\right. \\
\left.(S_0, S_5), (S_5,S_5) , (S_5,S_0)\right\}
\end{align}
\begin{equation}
\begin{split}
R = \{(S_1,S_1), (S_1,S_4), (S_4,S_4), (S_4,S_1), (S_2,S_2), (S_2,S_3), (S_3,S_3),\\ (S_3,S_2), (S_0,S_0), (S_0, S_5), (S_5,S_5) , (S_5,S_0)\}
\end{split}
\end{equation}
\end{document}
And here is a screen-shot of the second version (as the first version exceeds all possible limits...)
Best Answer
This can be set using TeX's paragraph settings as follows:
The image below shows the result.
To enter the break and have an automatic "[" inserted use the following short definition:
You can use it as follows:
Edit:
A different method closer to what the OP wants:
Ultimately the best method might be the one commented by Barbara, where one makes the space character active, but that is a job for after Christmas! The second method works well, but one has to be careful with the
\hsize
to get it to the right value to make the poems look right.