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Bibliographic Details
Main Authors: Harrison-Trainor, Matthew, Tan, Liam
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2604.17039
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Table of 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.