$σ$-Set Theory: Introduction to the concepts of $σ$-antielement, $σ$-antiset and Integer Space

Ivan Gatica Araus

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arXiv · 0906.3120

$σ$-Set Theory: Introduction to the concepts of $σ$-antielement, $σ$-antiset and Integer Space

Ivan Gatica Araus

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Abstract

In this paper we develop a theory called $σ$-Set Theory, in which we present an axiom system developed from the study of Set Theories of Zermelo-Fraenkel, Neumann-Bernays-Godel and Morse-Kelley. In $σ$-Set Theory, we present the proper existence of objects called $σ$-antielement, $σ$-antiset, natural numbers, antinatural numbers and generated $σ$-set by two $σ$-sets, from which we obtain, among other things, a commutative non-associative algebraic structure called Integer Space $3^{X}$, which corresponds to the algebraic completion of $2^{X}$.

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BibTeX RIS

Ivan Gatica Araus. 2010-09-25. $σ$-Set Theory: Introduction to the concepts of $σ$-antielement, $σ$-antiset and Integer Space. https://arxiv.org/abs/0906.3120

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