ABSTRACT
Invariant descriptive set theory is a new branch of descriptive set theory that deals with complexity of equivalence relations. On any Polish space there is always the identity equivalence relation (or the equality equivalence relation, that is, every element is equivalent to nothing but itself), and any subset of a Polish space is an invariant set for this equivalence relation. Therefore on a rather fundamental level invariant descriptive set theory encompasses and strengthens the classical and effective theories.
