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arXiv · 2312.11546

Set Theory is interpretable in Class Ordering Theory

Zuhair Al-Johar
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Abstract

Here it is shown that standard set theory can be interpreted in a theory about order. The ordering here is about non-extensional flat classes, i.e. classes that are not elements of classes. So, stipulating a nearly well order over all those classes coupled together with indexing that order by elements of those classes, thereby having those elements serve as ordinals; this together with infinity and a replacement like axiom would be shown to interpret ZFC. Moreover, it is shown that a suitable version of this order theory is bi-interpretable with Morse-Kelley set theory augmented with a well ordering on classes.

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Zuhair Al-Johar. 2023-12-16. Set Theory is interpretable in Class Ordering Theory. https://arxiv.org/abs/2312.11546

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