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Another New Foundation: A Theory with Combined Concepts from Set Theory, Type Theory and Leśniewski's Mereology

2016/09/12 by Jin Hoo Lee, Lee, Jin Hoo
Computer Science · Mathematics · #Advanced Algebra and Logic #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Rough Sets and Fuzzy Logic #math.LO

paper · pdf · doi:10.48550/arxiv.1609.03455

This paper has been withdrawn by the author due to a critical inconsiscency (approval of Cantor's paradox) found in the theory introduced in this article

openalex publication_date 2016/09/12 · arxiv created 2016/09/14 · arxiv updated 2016/09/15 · openalex created_date 2016/09/30 · openalex updated_date 2026/07/28

Abstract

This paper introduces a new theory which encompasses concepts and ideas from set theory, type theory, and Leśniewski's mereology and describes its possibility as an alternative foundation for mathematics. In the introduction section I will introduce motives for development of the theory and some remarks on the methods of presentation. Axioms of the theory and their philosophical background and justification on the basis of intuitive view are discussed next. Discussed after are realizations of mathematical concepts such as ℕ, ℤ, ℚ, ℝ, ℂ, etc. Then this paper concludes with comparisons between the theory and ZFC and its mathematical limitations.

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