Naive Axiomatic Mengenlehre for Experiments

TL;DR

This paper introduces Naive Axiomatic Mengenlehre (NAM), a framework for formalizing naive set theory by defining 'normal sets' through explicit criteria, and constructs related formal systems NAMix and NACT.

Contribution

It proposes a new axiomatic approach to naive set theory, formalizing the concept of normal sets and developing multiple systems to capture naive set theory intuitions.

Findings

Development of NAM system for formalizing normal sets

Construction of multiple NAMix systems as potential models of naive set theory

Introduction of NACT as a system of systems for naive axiomatic class theory

Abstract

The main goal of "Naive Axiomatic Mengenlehre" (NAM) is to find a more or less adequately explicit criterion that precisely formalizes the intuitive notion of a "normal set". NAM is mainly a construction procedure for building several formal systems NAMix, each of which can turn out to be an adequate codification of the contentual naive set theory. ("i" is a natural number which enumerates the used "normality" condition, and "x" is a letter which points to the variants of the used axioms.) Parallel to NAM, the Naive Axiomatic Class Theory NACT is constructed as a system of systems too.