Research Paper#Set Theory, Non-Founded Sets, Axiomatic Set Theory🔬 ResearchAnalyzed: Jan 3, 2026 20:20
Skands and Coskands: Exploring Non-Founded Set Theory
Published:Dec 26, 2025 11:02
•1 min read
•ArXiv
Analysis
This paper introduces and explores the concepts of 'skands' and 'coskands' within the framework of non-founded set theory, specifically NBG without the axiom of regularity. It aims to extend set theory by allowing for non-well-founded sets, which are sets that can contain themselves or form infinite descending membership chains. The paper's significance lies in its exploration of alternative set-theoretic foundations and its potential implications for understanding mathematical structures beyond the standard ZFC axioms. The introduction of skands and coskands provides new tools for modeling and reasoning about non-well-founded sets, potentially opening up new avenues for research in areas like computer science and theoretical physics where such sets may be relevant.
Key Takeaways
- •Introduces 'skands' and 'coskands' as new concepts in non-founded set theory.
- •Explores a modified NBG set theory without the axiom of regularity.
- •Aims to provide new tools for reasoning about non-well-founded sets.
- •Potentially relevant to areas like computer science and theoretical physics.
Reference
“The paper introduces 'skands' as 'decreasing' tuples and 'coskands' as 'increasing' tuples composed of founded sets, exploring their properties within a modified NBG framework.”