关于在算术形式中引入新的$θ$函数符号对设计能识别希尔伯特相容性片段的公理系统的意义
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
摘要：
提出了一种新的$θ$函数基元，它几乎达到了加法、乘法和后继增长运算的综合效率。这个$θ$函数符号使得能够构建一个“IQFS（PA+）”公理系统，该公理系统可以证实其自身希尔伯特一致性的不完整定义，同时它将同时验证所有Peano算术的$Π_1$定理的同构对应物。还建立了许多命题和中间结果。只有一个中间结果，大多数读者直觉上应该是正确的，仍然没有得到形式上的证明。
英文摘要：
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 $Π_1$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
