Set Theory and Logic

    

Scale-Relative Set Theory: A Unified Foundation for Mathematics and Physics

Authors: Daniel Nehmé

We introduce Scale-Relative Set Theory (SRST), a revolutionary framework where mathematical concepts are inherently relative to observational scales $kappa in mathbb{E}$. This theory naturally resolves classical paradoxes (Russell, Cantor, Burali-Forti), unifies arithmetic with geometry through a fundamental number-point isomorphism, and provides new foundations for topology, analysis, and modern physics. We develop complete scale-relative constructions of numerical sets, set operations, distance metrics, and neighborhood systems. The framework demonstrates profound connections to gauge theories, parallel transport, renormalization group flow, and quantum gravity. SRST explains how mathematical structures emerge across scales from quantum to cosmological, offering a unified understanding of reality that transforms both mathematical foundations and physical theory.

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[v1] 2025-10-30 20:23:19

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