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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.17039 |
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| _version_ | 1866913042670813184 |
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| author | Harrison-Trainor, Matthew Tan, Liam |
| author_facet | Harrison-Trainor, Matthew Tan, Liam |
| contents | A theory $T$ is said to be relatively decidable if for every model of $T$, one can compute the elementary diagram of that model from its atomic diagram together with $T$. We verify a conjecture of Chubb, Miller, and Solomon by showing that for complete theories $T$, $T$ is relatively decidable if and only if $T$ has a conservative model complete extension of the form $T \cup \{φ(\bar{c})\}$ where $T \models \exists \bar{x} \; φ(\bar{x})$. We also show that no such characterization works for incomplete theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17039 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characterizing relative decidability in terms of model completeness Harrison-Trainor, Matthew Tan, Liam Logic A theory $T$ is said to be relatively decidable if for every model of $T$, one can compute the elementary diagram of that model from its atomic diagram together with $T$. We verify a conjecture of Chubb, Miller, and Solomon by showing that for complete theories $T$, $T$ is relatively decidable if and only if $T$ has a conservative model complete extension of the form $T \cup \{φ(\bar{c})\}$ where $T \models \exists \bar{x} \; φ(\bar{x})$. We also show that no such characterization works for incomplete theories. |
| title | Characterizing relative decidability in terms of model completeness |
| topic | Logic |
| url | https://arxiv.org/abs/2604.17039 |