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CHERNIKOV, ARTEM
and
MENNEN, ALEX
2023.
SEMI-EQUATIONAL THEORIES.
The Journal of Symbolic Logic,
p.
1.
Published online by Cambridge University Press: 15 July 2020
A first-order theory is equational if every definable set is a Boolean combination of instances of equations, that is, of formulae such that the family of finite intersections of instances has the descending chain condition. Equationality is a strengthening of stability. We show the equationality of the theory of proper extensions of algebraically closed fields and of the theory of separably closed fields of arbitrary imperfection degree.