Hyperfinite and standard unifications for physical theories

Abstract

A set of physical theories is represented by a nonempty subset {SNjV|j∈ℕ} of the lattice of consequence operators defined on a language Λ. It is established that there exists a unifying injection 𝒮 defined on the nonempty set of significant representations for natural systems M⊂Λ. If W∈M, then 𝒮W is a hyperfinite ultralogic and ⋃{SNjV(W)|j∈ℕ}=𝒮W(*W)∩Λ. A “product” hyperfinite ultralogic Π is defined on internal subsets of the product set *Λm and is shown to represent the application of 𝒮 to {W1,…,Wm}⊂M. There also exists a standard unifying injection SW such that 𝒮W(*W)⊂*SW(*W).