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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.21954 |
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Table of 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.