# Definition:Principle of General Induction/Minimally Closed Class/Terminology

## Terminology of Principle of General Induction for Minimally Closed Class

### Basis for the Induction

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

### Induction Hypothesis

The assumption made that $\map P x$ is true for some $x \in M$ is called the induction hypothesis.

### Induction Step

The step which shows that $\map P x = \T \implies \map P {\map g x} = \T$ is called the induction step.