On the logical structure of some maximality and well-foundedness principles equivalent to choice principles
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866911878480920576 |
|---|---|
| author | Herbelin, Hugo |
| author_facet | Herbelin, Hugo |
| contents | We study the logical structure of Teichm{ü}ller-Tukey lemma, a maximality principle equivalent to the axiom of choice and show that it corresponds to the generalisation to arbitrary cardinals of update induction, a well-foundedness principle from constructive mathematics classically equivalent to the axiom of dependent choice.From there, we state general forms of maximality and well-foundedness principles equivalent to the axiom of choice, including a variant of Zorn's lemma. A comparison with the general class of choice and bar induction principles given by Brede and the first author is initiated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09946 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the logical structure of some maximality and well-foundedness principles equivalent to choice principles Herbelin, Hugo Logic in Computer Science Logic We study the logical structure of Teichm{ü}ller-Tukey lemma, a maximality principle equivalent to the axiom of choice and show that it corresponds to the generalisation to arbitrary cardinals of update induction, a well-foundedness principle from constructive mathematics classically equivalent to the axiom of dependent choice.From there, we state general forms of maximality and well-foundedness principles equivalent to the axiom of choice, including a variant of Zorn's lemma. A comparison with the general class of choice and bar induction principles given by Brede and the first author is initiated. |
| title | On the logical structure of some maximality and well-foundedness principles equivalent to choice principles |
| topic | Logic in Computer Science Logic |
| url | https://arxiv.org/abs/2405.09946 |