Abstract
Let L be a finite pseudocomplemented lattice. Every interval [0, a] in L is pseudocomplemented, so by Glivenko’s theorem, the set S(a) of all pseudocomplements in [0, a] forms a boolean lattice. Let Bi denote the finite boolean lattice with i atoms. We describe all sequences (s0, s1, . . . , sn) of integers for which there exists a finite pseudocomplemented lattice L with si = |{ a ∈ L | S(a) ≅ Bi}|, for all i, and there is no a ∈ L with S(a) ≅ Bn+1. This result settles a problem raised by the first author in 1971.
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