Abstract

The quasiorders of a setA form a lattice Quord(A) with an involution ρ↦ρ−1={〈x, y〉: 〈y, x〉∈ρ}. Some results in [1] and Chajda and Pinus [2] lead to the problem whether every lattice with involution can be embedded in Quord(A) for some setA. Using the author's approach to the word problem of lattices (cf. [3]), which also applies for involution lattices, it is shown that the answer is negative.

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