数学基础的关系公理化框架
A Relational Axiomatic Framework for the Foundations of Mathematics
摘要：
我们提出了一个基于一元关系概念的关系演算。在这个关系演算中，不同的公理系统收敛到一个称为动态生成系统与对称（DGSS）的模型。在DGSS中，我们定义了关系集和函数的概念，证明了扩张性和等式的替换性是DGSS的定理。作为DGSS的第一个例子，我们构造了一个自然数模型，而不依赖于Peano公理。最后，对零的性质给出了一些新的解释。
英文摘要：
We propose a Relational Calculus based on the concept of unary relation. In this Relational Calculus different axiomatic systems converge to a model called Dynamic Generative System with Symmetry (DGSS). In DGSS we define the concepts of relational set and function and prove that extensionality and the substitution property of equality are theorems of DGSS. As a first exemplification of DGSS, we construct a model of natural numbers without relying on Peano's Axioms. Eventually, some new clarifications regarding the nature of the number zero are given.
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