Uniform terms and local elements

TL;DR

This paper investigates the structure of function terms in uniform theories, connecting algebraic, field, and measure theories, and introduces a novel interpretation of elements as automorphisms with a localization method.

Contribution

It offers a new interpretation of elements as automorphisms and proposes a localization method, advancing the understanding of uniform theories and their algebraic properties.

Findings

Connection between uniform theories and field/measure theory

Automorphism-based interpretation of elements

Method for localizing elements relative to each other

Abstract

The article explores function terms within uniform theories. It examines the uniformity of these theories through an algebraic lens. The paper compares the uniformity of terms and predicates within axiom schemas. It demonstrates the connection between such theories and both field theory and measure theory. The work proposes a novel interpretation of elements as automorphisms of the sets that include them. Additionally, it introduces a method for the localization of elements in relation to one another. Uniform Terms and Local Elements, 2024, msc: 03G30, 03H99 Key words: Terms and predicates, singletons, sections, automorphisms, translation group, Galois correspondence, uniformity and non-uniformity.