A Quest for the Existence of Bi-Conditional Statements Over the Theory of a Model

Abstract: Construction of the group of all bi-conditional statements over the theory of a model and discussing its properties and isomorphic forms for the quest and experiments of the existence of the converse of a statement over that model irrespective of its individual proof.

Keywords: Theory of a model, join as a logical connective, group of if statements, non-divisible infinite abelian group, infinite symmetric and permutation groups.