Submission date: 18 September 2021

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 for every M ⪯ N ⊩ T, there is an absolute bound on the number of types realized in N-M over M.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 2109.08943: pdf, ps.