Notes on Interpretability between Weak First-order Theories: Theories of Sequences

Lars Kristiansen; Juvenal Murwanashyaka

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arXiv · 2402.14286

Notes on Interpretability between Weak First-order Theories: Theories of Sequences

Lars Kristiansen·Juvenal Murwanashyaka

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Abstract

We introduce a first-order theory $\mathsf{Seq}$ which is mutually interpretable with Robinson's $\mathsf{Q}$. The universe of a standard model for $\mathsf{Seq}$ consists of sequences. We prove that $\mathsf{Seq}$ directly interprets the adjuctive set theory $\mathsf{AST}$, and we prove that $\mathsf{Seq}$ interprets the tree theory $\mathsf{T}$ and the set theory $\mathsf{AST + EXT}$.

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Lars Kristiansen, Juvenal Murwanashyaka. 2024-02-22. Notes on Interpretability between Weak First-order Theories: Theories of Sequences. https://arxiv.org/abs/2402.14286

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