EDIT: I cross-posted this, and couldn't delete this one as it had some answers. There is a good answer at: https://cs.stackexchange.com/a/53056/46284
$\exists x \in \Sigma^* (t=sx)$
Have I interpreted the above into words correctly?:
"There exists a symbol 'x', which is a member of the set which contains all possible strings of alphabet sigma, where sigma contains string 't', which is a concatenation of string x and string s."
I'm not clear on how/whether t=xs is an alphabet.
(Since this question relates to logical notation, the math stack exchange seemed like not the worst place to ask, (and the theo-sci-comp stack was for researchers); sorry if this is in the wrong place. If anyone knows a better place to ask, please let me know.)
There is a $\in$ symbol missing, but otherwise it looks like the definition of a suffix of a word. Here is my interpretation:
Definition. Let $t$ be of word of $\Sigma^*$. Then a word $s \in \Sigma^*$ is a suffix of $t$ if there exists a word $x \in \Sigma^*$ such that $t = xs$. (With a logical formula: $\exists x \in \Sigma^* \ t = xs$).