Definition:Principle of General Induction/Minimally Closed Class/Basis for the Induction

Terminology of Principle of General Induction for Minimally Closed Class

Consider a Proof by General Induction for a minimally closed class under $g$ with respect to $b$.

The step that shows that the propositional function $P$ holds for the distinguished $b \in M$ is called the basis for the induction.

Also known as

The basis for the induction is often informally referred to as the base case.