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Given a classic (not Residuated) lattice, with standard definition of partial order via lattice join and meet operations, is it possible to satisfy Galois equivalence

(x v y) < z <-> x < (y / z).

for some binary operation /?

Edit: One way to answer this is putting lattice axioms together with Galois condition into something like Mace4. Then finite model search reveals that lattice join v appears to have no adjoints, while meet ^ has. The question is more subtle, however: is there adjoint for lattice meet operation in any lattice model?

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Consider what happens when $y>z$. You cannot dualize only some parts of the definition of a Heityng algebra and blindly hope to obtain something useful. – user46855 Feb 16 '14 at 22:07

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