Submission date: 22 July 2021

Abstract:

Given a complete theory T and a subset Y ⊆ X^k, we precisely determine the worst case complexity of an expansion (M,Y) by Y of a model M of T with universe X. Although by definition monadically stable/NIP theories remain tame under arbitrary monadic expansions, we show that monadically NFCP (equivalently, mutually algebraic) theories are the largest class robust under anything beyond monadic expansions. We also exhibit a paradigmatic structure for the failure of each of these monadic properties, and prove each of these paradigms definably embeds into a monadic expansion of a sufficiently saturated model of any theory without the corresponding property.

Mathematics Subject Classification:

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Full text arXiv 2107.10920: pdf, ps.