On How the Introducing of a New θ Function Symbol Into Arithmetic's Formalism Is Germane to Devising Axiom Systems that Can Appreciate Fragments of Their Own Hilbert Consistency
Abstract
A new θ function primitive is proposed that almost achieves the combined efficiency of the addition, multiplication and successor growth operations. This θ 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 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.
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