The Notion "Pathology" in Set Theory

Details The Notion "Pathology" in Set Theory The Notion "Pathology" in Set Theory

2008-07-27

arxiv.org/abs/0807.4321v1

Mathematics

Logic

21 pages, no figures

Scientific paper

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).

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