A Suslin scheme is a family of subsets of a set indexed by finite sequences of non-negative integers. The Suslin operation applied to this scheme produces the set
Alternatively, suppose we have a Suslin scheme, in other words a function from finite sequences of positive integers to sets . The result of the Suslin operation is the set
where the union is taken over all infinite sequences
If is a family of subsets of a set , then is the family of subsets of obtained by applying the Suslin operation to all collections as above where all the sets are in .
The Suslin operation on collections of subsets of has the property that . The family is closed under taking countable unions or intersections, but is not in general closed under taking complements.
If is the family of closed subsets of a topological space, then the elements of are called Suslin sets, or analytic sets if the space is a Polish space.