Relative consistency of a finite nonclassical theory incorporating ZF and category theory with ZF
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866914387046957056 |
|---|---|
| author | Cabbolet, Marcoen J. T. F. Mathias, Adrian R. D. |
| author_facet | Cabbolet, Marcoen J. T. F. Mathias, Adrian R. D. |
| contents | Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foundational theory for (all of) mathematics that is not weaker than ZF, that is finitely axiomatized, and that does not have a countable model (if it has a model at all, that is). Here we prove that T is relatively consistent with ZF. We conclude that this is an important step towards showing that T is an advancement in the foundations of mathematics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_18969 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relative consistency of a finite nonclassical theory incorporating ZF and category theory with ZF Cabbolet, Marcoen J. T. F. Mathias, Adrian R. D. General Mathematics Recently, in Axioms 10(2): 119 (2021), a nonclassical first-order theory T of sets and functions has been introduced as the collection of axioms we have to accept if we want a foundational theory for (all of) mathematics that is not weaker than ZF, that is finitely axiomatized, and that does not have a countable model (if it has a model at all, that is). Here we prove that T is relatively consistent with ZF. We conclude that this is an important step towards showing that T is an advancement in the foundations of mathematics. |
| title | Relative consistency of a finite nonclassical theory incorporating ZF and category theory with ZF |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2407.18969 |