Set Theory Axioms Using Explication

TL;DR

This paper introduces a new set theory called Explication, which combines features from existing systems and provides a complete axiomatic framework starting from class variables to sets.

Contribution

It presents a comprehensive axiomatic system for Explication, a novel set theory that explicitly characterizes classes and sets through finite statements.

Findings

Complete axiomatization of Explication set theory

Explicit identification of classes as sets

Framework for finite statement membership

Abstract

This paper provides a complete suite of axioms for a version of set theory that I call Explication. Explication borrows from the two most prominent existing systems of set theory. Explication starts with class variables. After several steps, some of these class variables are identified as sets. The most crucial step is to identify classes which can explicitly say, in a finite statement, which other classes are its members. The reader is cautioned that the suite of axioms presented is a complete treatment of Explication. Statements which may or may not be true in other axiom systems are not significant.