Cartagena Logic
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2021
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866913226360356864 |
|---|---|
| author | Kivimäki, Siiri Väänänen, Jouko Villaveces, Andrés |
| author_facet | Kivimäki, Siiri Väänänen, Jouko Villaveces, Andrés |
| contents | We introduce a new kind of infinitary logic that we call Boolean expansion of ${\mathcal L}_{κκ}$. This logic involves a new kind of variable, that we call generalised Boolean variable. These variables range over the powerset of a cardinal number in a way reminiscent of random variables. From this Boolean expansion, we extract a traditional infinitary logic, called Cartagena logic. We prove several model-theoretic properties of Cartagena logic, and give multiple examples of its expressive power. The main result is that Cartagena logic is a good syntactically defined approximation to Shelah's infinitary ${\mathcal L}^1_κ$. The latter is not known to have a generative syntax, while Cartagena logic does have a very clear one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_13495 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Cartagena Logic Kivimäki, Siiri Väänänen, Jouko Villaveces, Andrés Logic 03C40, 03C55, 03C75, 03C95 We introduce a new kind of infinitary logic that we call Boolean expansion of ${\mathcal L}_{κκ}$. This logic involves a new kind of variable, that we call generalised Boolean variable. These variables range over the powerset of a cardinal number in a way reminiscent of random variables. From this Boolean expansion, we extract a traditional infinitary logic, called Cartagena logic. We prove several model-theoretic properties of Cartagena logic, and give multiple examples of its expressive power. The main result is that Cartagena logic is a good syntactically defined approximation to Shelah's infinitary ${\mathcal L}^1_κ$. The latter is not known to have a generative syntax, while Cartagena logic does have a very clear one. |
| title | Cartagena Logic |
| topic | Logic 03C40, 03C55, 03C75, 03C95 |
| url | https://arxiv.org/abs/2108.13495 |