A Relational Axiomatic Framework for the Foundations of Mathematics

Details A Relational Axiomatic Framework for the Foundations of Mathematics A Relational Axiomatic Framework for the Foundations of Mathematics

2010-01-25

arxiv.org/abs/1001.4380v1

Mathematics

General Mathematics

Scientific paper

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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