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Is there published work about universal anti-Horn classes? Anti-Horn formulas are also sometimes known as dual Horn. See also related question Is there any research of universal algebras axiomatized ...

Let $M=(W,R)$ be a Kripke frame, $A=(f_1,...,f_m)$ is a tuple of operations $f_i:W^{n_i}\to W$, and $\Phi=(\varphi_1,...,\varphi_m )$ is a tuple of first-order logic formulas in vocabulary $\sigma=\{=...