International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 2, Pages 93-102
doi:10.1155/S0161171201006913
Hyperfinite and standard unifications for physical theories
Mathematics Department, U. S. Naval Academy, 572C Holloway RD, Annapolis 21402-5002, MD, USA
Received 1 March 2001
Copyright © 2001 Robert A. Herrmann. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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).