Definiteness properties of first-order schemes
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866908677696389120 |
|---|---|
| author | Gruza, Piotr Łełyk, Mateusz |
| author_facet | Gruza, Piotr Łełyk, Mateusz |
| contents | The paper aims to establish a convenient formal framework for investigating the phenomenon of scheme definiteness, exemplified by first-order internal categoricity as studied by Väänänen, among others. To this end, we introduce the notion of $Φ$-definiteness, thereby refining and extending the conceptual landscape that underlies various first-order categoricity notions in the literature (internal categoricity, strong internal categoricity, intolerance). We provide arguments for the robustness of our definition and present examples of schemes that separate different categoricity- and completeness-like notions. Finally, we offer a brief glimpse into the issue of the definiteness of two canonical foundational schemes - the induction scheme and the replacement scheme. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_21954 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Definiteness properties of first-order schemes Gruza, Piotr Łełyk, Mateusz Logic The paper aims to establish a convenient formal framework for investigating the phenomenon of scheme definiteness, exemplified by first-order internal categoricity as studied by Väänänen, among others. To this end, we introduce the notion of $Φ$-definiteness, thereby refining and extending the conceptual landscape that underlies various first-order categoricity notions in the literature (internal categoricity, strong internal categoricity, intolerance). We provide arguments for the robustness of our definition and present examples of schemes that separate different categoricity- and completeness-like notions. Finally, we offer a brief glimpse into the issue of the definiteness of two canonical foundational schemes - the induction scheme and the replacement scheme. |
| title | Definiteness properties of first-order schemes |
| topic | Logic |
| url | https://arxiv.org/abs/2511.21954 |