Theories with few non-algebraic types over models, and their decompositions

Autor: Braunfeld, Samuel, Laskowski, Michael C
Rok vydání: 2021
Předmět:
Zdroj: Proc. Amer. Math. Soc. 150 (2022), 4021-4026
Druh dokumentu: Working Paper
DOI: 10.1090/proc/15956
Popis: We consider several ways of decomposing models into parts of bounded size forming a congruence over a base, and show that admitting any such decomposition is equivalent to mutual algebraicity at the level of theories. We also show that a theory $T$ is mutually algebraic if and only if there is a uniform bound on the number of coordinate-wise non-algebraic types over every model, regardless of its cardinality.
Comment: 6 pages; to appear in Proceedings of the AMS
Databáze: arXiv