Definition:Principle of Superinduction/Terminology

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Terminology of Principle of Superinduction

Basis for the Induction

The step that shows that the propositional function $P$ holds for $\O$ 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.


Closure under Chain Unions

The step which shows that:

$\ds \forall C: \forall x \in C = \map P x = \T \implies \map P {\bigcup C} = \T$

is called the closure under chain unions.