[2304.00581] Generalized Von Neumann Universe and Non-Well-Founded Sets Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Mathematics > Logic arXiv:2304.00581 (math) [Submitted on 2 Apr 2023 ( v1 ), last revised 25 Apr 2026 (this version, v3)] Title: Generalized Von Neumann Universe and Non-Well-Founded Sets Authors: Eugene Zhang View a PDF of the paper titled Generalized Von Neumann Universe and Non-Well-Founded Sets, by Eugene Zhang View PDF HTML (experimental) 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. Comments: Submitted to Journal of Symbolic Logic in September 2020; v1 submitted in March 2019; 64 pages, 4 figures Subjects: Logic (math.LO) MSC classes: 03C55, 03C75, 03E99 Cite as: arXiv:2304.00581 [math.LO] (or arXiv:2304.00581v3 [math.LO] for this version) https://doi.org/10.48550/arXiv.2304.00581 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Eugene Zhang [ view email ] [v1] Sun, 2 Apr 2023 17:34:43 UTC (333 KB) [v2] Wed, 3 Dec 2025 03:46:16 UTC (338 KB) [v3] Sat, 25 Apr 2026 10:16:06 UTC (348 KB) Full-text links: Access Paper: View a PDF of the paper titled Generalized Von Neumann Universe and Non-Well-Founded Sets, by Eugene Zhang View PDF HTML (experimental) TeX Source view license Current browse context: math.LO < prev | next > new | recent | 2023-04 Change to browse by: math References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from