Semi-equational theories

2022/04/28 by Artem Chernikov, Chernikov, Artem, Alex Mennen +1
Mathematics · #03C45 #Advanced Topology and Set Theory #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2204.13790

openalex publication_date 2022/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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