On the Uniqueness of Minimal Physically Derivable Theories

This paper proves a metatheorem concerning the class of physical theories derivable from minimal axiom sets. Rather than asking whether two given theories are equivalent — the direction taken by the existing literature on theoretical equivalence — it asks a prior question: given a set of conditions on minimality, is there more than one theory that can satisfy them? The answer established here is no. Four independently motivated conditions on minimal axiom sets are identified: a single fundamental indivisible and immutable constituent of matter; space represented as a computationally finite object, excluding the mathematical continuum; momentum as a primitive, intrinsic, and conserved property of fundamental…