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:
  1. The set being defined is the smallest set that satisfies the basis and inductive clauses.
  2. The set being defined is the intersection of all the set that satisfy the basis and inductive clauses.
  3. 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.