Set Theory is interpretable in Class Ordering Theory
| Autor: | Al-Johar, Zuhair |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 12 pages |
| Databáze: | arXiv |
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