Recursive Definition
Variations of Extremal Clause
Variations of Extremal Clause
The extremal clause of a recursive definition can be stated in a variety of equivalent ways such as:
- The set being defined is the smallest set that satisfies the basis and inductive clauses.
- The set being defined is the intersection of all the set that satisfy the basis and inductive clauses.
- No proper subset of the set being defined satisfies the basis and inductive clauses.
These are all equivalent and you can use any of them as an extremal clause.