Bisimulations of potentialist systems

Sam Adam-Day

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arXiv · 2206.10359

Bisimulations of potentialist systems

Sam Adam-Day

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Abstract

A potentialist system is a first-order Kripke model based on embeddings. I define the notion of bisimulation for these systems, and provide a number of examples. Given a first-order theory $T$, the system $\mathrm{Mod}(T)$ consists of all models of $T$. We can then take either all embeddings, or all substructure inclusions, between these models. I show that these two ways of defining $\mathrm{Mod}(T)$ are bitotally bisimilar. Next, I relate the notion of bisimulation to a generalisation of the Ehrenfeucht-Fra\"is\'e game, and use this to show the equivalence of the existence of a bisimulation with elementary equivalence with respect to an infinitary language. Finally, I consider the question of when a potentialist system is bitotally bisimilar to a system containing set-many models, providing too different sufficient conditions.

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BibTeX RIS

Sam Adam-Day. 2022-06-21. Bisimulations of potentialist systems. https://arxiv.org/abs/2206.10359

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