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It is well-known that the self-dual class of all distributive lattices class is definable by the single self-dual equation xy+yz+zx = (x+y)(y+z)(z+x) and similarly the self-dual class of all modular lattices is definable by the self-dual equation (x+y)(z+xy) = xy + z(x+y). Given a finitely based self-dual variety of lattices, one might ask if it is definable by a single self-dual lattice equation (modulo, lattice theory). Making use of several methods for producing a single identity which is equivalent to a finite set of given identities, we show that there are infinitely many self-dual lattice varieties with "yes'' as the answer. In particular, we show that every finitely based self-dual subvariety of modular lattices is definable by a single self-dual equation. Also there are infinitely many finitely based self-dual lattice varieties which are not so definable. These results were obtained in collaboration with David Kelly.

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