The Notion "Pathology" in Set Theory
Logic
2008-07-29 v1
Abstract
When we study the paradoxes of set theory we find out that there are mainly 2 types: the pathologies and the antinomies. These 2 notions are made precise and compared with the somehow inductively definable concept "abnormal". (See my paper "Naive Axiomatic Mengenlehre for Experiments" in arXiv.) In the following 5 Patho Theses are discussed in order to formalize this notion of pathology. This allows us to define formally the property "Hereditary-non-Pathological" for well-formed formulas. With this property the system NACT* of Naive Axiomatic Class Theory is constructed, which has a "unique maximal" universe (in a special sense).
Keywords
Cite
@article{arxiv.0807.4321,
title = {The Notion "Pathology" in Set Theory},
author = {Werner DePauli-Schimanovich},
journal= {arXiv preprint arXiv:0807.4321},
year = {2008}
}
Comments
21 pages, no figures