International Journal of Mathematics and Mathematical Sciences
Volume 28 (2001), Issue 2, Pages 93-102

Hyperfinite and standard unifications for physical theories

Robert A. Herrmann

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.


A set of physical theories is represented by a nonempty subset {SNjV|j} 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 MΛ. If WM, then 𝒮W is a hyperfinite ultralogic and {SNjV(W)|j}=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).