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Semi-equational theories

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arxiv 2204.13790 v2 pith:KKSNYWHY submitted 2022-04-28 math.LO

Artem Chernikov , Alex Mennen This is my paper
classification math.LO
keywords semi-equationaltheoriesweaklyalgebraicallycertainclosedconnectioncontext
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We introduce and study semi-equational and weakly semi-equational theories, generalizing equationality in stable theories (in the sense of Srour) to the NIP context. In particular, we establish a connection to distality via one-sided strong honest definitions; demonstrate that certain trees are semi-equational, while algebraically closed valued fields are not weakly semi-equational; and obtain a general criterion for weak semi-equationality of an expansion of a distal structure by a new predicate.

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Cited by 1 Pith paper

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  1. Externally definable fsg groups in NIP theories

    math.LO 2025-06 accept novelty 8.0 of 10

    Every fsg group externally definable in an NIP structure is definably isomorphic to a group interpretable in that structure.

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