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Worst Case Expansions of Complete Theories by Braunfeld, Samuel; Laskowski, Michael C. is a scholarly article available to read on EtoBox.

What is Worst Case Expansions of Complete Theories about?

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

Author

Braunfeld, Samuel; Laskowski, Michael C.

Published

2021

Language

EN