Standard and Hyperfinite Unifications for All Physical Theories

Abstract

In this paper, the set of all physical theories is represented by a countable subset of the lattice of consequence operators defined on a language L. It is established that there exists a unifying injection U defined on the set of significant representations for natural-systems M. If W is a member of M, then U selects an ultralogic C such that C(*W) restricted to L is a unification for the set of all physical theories as each is applied to W. There also exists a standard injection S that for each W in M selects a standard unifying consequence operator D, where C(*W) is a subset of *D(*W). It is also shown how to use these unifying operators and obtain a product operator that has the same effect but, in a practical sense, this operator is applied to every natural-system within our universe simultaneously.