On How the Introducing of a New $\theta$ Function Symbol Into Arithmetic's Formalism Is Germane to Devising Axiom Systems that Can Appreciate Fragments of Their Own Hilbert Consistency

Abstract

A new $\theta$ function primitive is proposed that almost achieves the combined efficiency of the addition, multiplication and successor growth operations. This $\theta$ function symbol enables the constructing of an "IQFS(PA+)" axiom system that can corroborate a fragmentary definition of its own Hilbert consistency, while it will simultaneously verify isomorphic counterparts of all Peano Arithmetic's ${\Pi }_1$ theorems. Many propositions and intermediate results are also established. Only one intermediate result, which most readers will intuit should be true, does remain formally unproven.

arXiv commentAll the theorems and propositons are the same in this Version 5 as in Version 4. The difference is that the writing style is now significantly more polished