2024/05/06 by Tapani Hyttinen, Hyttinen, Tapani, Joni Puljujärvi +3
Computer Science · Engineering · #03C45 #03C48 #03C85 #Computer Graphics and Visualization Techniques #FOS: Mathematics #Logic (math.LO) #Slime Mold and Myxomycetes Research
paper · pdf · doi:10.48550/arxiv.2405.03785
openalex publication_date 2024/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Motivated by team semantics and existential second-order logic, we develop a model-theoretic framework for studying second-order objects such as sets and relations. We introduce a notion of abstract elementary team categories that generalizes the standard notion of abstract elementary class, and show that it is an example of an accessible category. We apply our framework to show that the logic FOT introduced by Kontinen and Yang satisfies a version of Lindström's Theorem. Finally, we consider the problem of transferring categoricity between different cardinalities for complete theories in existential second-order logic (or independence logic) and prove both a downwards and an upwards categoricity transfer result.