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Preprint Number 2054

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2054. Michael C Laskowski
Theories admitting congruences over sets and boundedness

Submission date: 18 September 2021


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.

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