Full Idea
{x; A(x)} indicates a set of objects which satisfy the condition A(x).
Clarification
[some logicians use a vertical bar {a|A(x)} or a colon {a:A(x)} instead of the semi-colon]
Gist of Idea
{x; A(x)} is a set of objects satisfying the condition A(x)
Source
Graham Priest (Intro to Non-Classical Logic (1st ed) [2001], 0.1.2)
Book Reference
Priest,Graham: 'Introduction to Non-Classical Logic' [CUP 2001], p.-7