SEMI-EQUATIONAL THEORIES

Artem Chernikov, Alex Mennen

Type: Article

Publication Date: 2023-05-10

Citations: 1

DOI: https://doi.org/10.1017/jsl.2023.28

Abstract

Abstract We introduce and study (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.

Locations

Journal of Symbolic Logic - View
arXiv (Cornell University) - View - PDF

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Works Cited by This (31)

Action	Title	Year	Authors
+	Vapnik-Chervonenkis density in some theories without the independence property, I	2015	Matthias Aschenbrenner Alf Dolich Deirdre Haskell Dugald Macpherson Sergei Starchenko
+ PDF Chat	On VC-minimal theories and variants	2013	Vincent Guingona M. Laskowski
+ PDF Chat	Countable models of stable theories	1983	Anand Pillay
+ PDF Chat	Logical stability in group theory	1976	John T. Baldwin Jan Saxl
+	The notion of independence in categories of algebraic structures, part I: Basic properties	1988	Gabriel Srour
+	A trichotomy theorem for o-minimal structures	1998	Ya’acov Peterzil Sergei Starchenko
+	Externally definable sets and dependent pairs II	2015	Artem Chernikov Pierre Simon
+	The notion of independence in categories of algebraic structures, part II: S-minimal extensions	1988	Gabriel Srour
+	The notion of independence in categories of algebraic structures, part III: equational classes	1990	Gabriel Srour
+	Linear O-minimal structures	1993	James Loveys Ya’acov Peterzil