We generalize the definition of an Induction Model given by L. Henkin (1960). The main goal of the paper is to study reduction and equivalence between these Induction Models. We give a formal definition for these concepts and then prove a criterion which can be used to check when one Induction Model can be reduced to or is equivalent to another Induction Model.

We also look at the base cases and generating functions which can give us an Induction Model. There are three cases which we look at depending on the structure of the generating functions (arbitrary, additive, multiplicative).