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A Relational Axiomatic Framework for the Foundations of Mathematics

2010/01/25 by Lidia Obojska, Obojska, Lidia
Computer Science · Psychology · #03G27 #03H05 #18A15 #Advanced Algebra and Logic #FOS: Mathematics #General Mathematics (math.GM) #Logic, Reasoning, and Knowledge #Philosophy and Theoretical Science

paper · pdf · doi:10.48550/arxiv.1001.4380

openalex publication_date 2010/01/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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