2020/11/28 by Anthony D'Arienzo, D'Arienzo, Anthony, Vinny Pagano +3
Computer Science · #03A10 #03B20 #03G30 (Primary) #18C10 #18C50 #18E08 #18N10 #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Logic (math.LO) #Logic, Reasoning, and Knowledge #Logic, programming, and type systems
paper · pdf · doi:10.48550/arxiv.2011.14056
openalex publication_date 2020/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of coherent theories and the (strict) bicategory of coherent categories. While the biequivalence concerns the stronger equality-preserving bi-interpretability, we use it to obtain a necessary and sufficient condition for two theories to be bi-interpretable in general, by relating the exact completions of their syntactic categories. These results extend analogously to familiar fragments of first-order logic, thereby clarifying the long-intuited relation between logical syntax and syntactic categories.