The calculus of relations as a foundation for mathematics

A variable-free, equational logic L-x based on the calculus of relations ( a theory of binary relations developed by DeMorgan, Peirce, and Schroder during the period 1864 - 1895) is shown to provide an adequate framework for the development of all of mathematics. The expressive and deductive powers of L-x are equivalent to those of a system of first-order logic with just three variables. Therefore, three-variable first-order logic also provides an adequate framework for mathematics. Finally, it is shown that a variant of L-x may be viewed as a subsystem of sentential logic. Hence, there are subsystems of sentential logic that are adequate to the task of formalizing mathematics.