Nondefinability of projectivity in lattice varieties (Q790855)

By showing how projectivities and weak projectivities can be built into lattice identities the author created one of the most important tools in the equational theory of lattices. Though, as he shows in the note under review, neither concept is first order definable in any lattice variety other than distributive lattices. In contrast, for any finite lattice there is a bound on the length of weak projectivities needed for the description of principal congruences in the associated variety.