Generalized Von Neumann Universe and Non-Well-Founded Sets

Eugene Zhang

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arXiv · 2304.00581

Generalized Von Neumann Universe and Non-Well-Founded Sets

Eugene Zhang

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Abstract

In this paper, a generalized version of the von Neumann universe known as the total universe is proposed to formally introduce non-well-founded sets that include infinitons, semi-infinitons and quasi-infinitons in Russell's paradox. All three infinitons are part of infinitely generated sets that are generators of non-well-founded sets. Combining the well-founded sets with the non-well-founded sets, the total universe is a model of ZF minus the axiom of regularity and free of Russell's paradox. The axiom of regularity can not define the well-founded sets and is invalid in any system consistent with ZF set theory.

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BibTeX RIS

Eugene Zhang. 2023-04-02. Generalized Von Neumann Universe and Non-Well-Founded Sets. https://arxiv.org/abs/2304.00581

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