Theories with few non-algebraic types over models, and their decompositions
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- by Samuel Braunfeld and Michael C. Laskowski PDF
- Proc. Amer. Math. Soc. 150 (2022), 4021-4026 Request permission
Abstract:
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.References
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Additional Information
- Samuel Braunfeld
- Affiliation: Faculty of Mathematics and Physics, Computer Science Institute, Charles University, Praha 11800, Czechia
- MR Author ID: 1197349
- Michael C. Laskowski
- Affiliation: Department of Mathematics, University of Maryland College Park, College Park, Maryland 20742
- MR Author ID: 110500
- Received by editor(s): September 18, 2021
- Received by editor(s) in revised form: December 14, 2021
- Published electronically: April 14, 2022
- Additional Notes: The second author was partially supported by NSF grant DMS-1855789
- Communicated by: Vera Fischer
- © Copyright 2022 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 150 (2022), 4021-4026
- MSC (2020): Primary 03C45
- DOI: https://doi.org/10.1090/proc/15956
- MathSciNet review: 4446248