  Mathematical induction is a fundamental tool in computer science and
mathematics. Henkin initiated the study of formalization of mathematical
induction restricted to the setting when the base case B is set to singleton
set containing 0 and a unary generating function S. The usage of mathematical
induction often involves wider set of base cases and k-ary generating functions
with different structural restrictions. While subsequent studies have shown
several Induction Models to be equivalent, there does not exist precise logical
characterization of reduction and equivalence among different Induction Models.
In this paper, we generalize the definition of Induction Model and demonstrate
existence and construction of S for given B and vice versa. We then provide a
formal characterization of the reduction among different Induction Models that
can allow proofs in one Induction Models to be expressed as proofs in another
Induction Models. The notion of reduction allows us to capture equivalence
among Induction Models.

Logic in Computer Science