the problem whether every lattice of cardinality ℵ 1 , in the variety generated by M 3 , has a congruence m-permutable, congruence-preserving extension for some positive integer m (Gillibert [21]); -a 1962 problem by Jónsson about coordinatizability of sectionally complemented modular lattices without unit (Wehrung [69]).Example 1-1.5. For a (∨, 0)-semilattice S, an S-valued distance on a set Ω is a map δ : Ω × Ω → S such that δ(x, x) = 0 , δ(x, y) = δ(y, x) , δ(x, z) ≤ δ(x, y) ∨ δ(y, z) (triangular inequality),