Decision problem for the first order theory of free objects in equational classes of algebras was investigated for groups (Malcev ), semigroups (Quine ), commutative semigroups (Mostowski ), distributive lattices (Ershov ) and several varieties of rings (Lavrov ). Recently this question was solved for all varieties of Hilbert algebras and distributive pseudo-complemented lattices (see , ). In this paper we prove that the theory of all finitely generated free pseudo-complemented semilattices is undecidable.
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Pawel M. Idziak, Undecidability of Free Pseudo-Complemented Semilattlces. Publ. Res. Inst. Math. Sci. 23 (1987), no. 3, pp. 559–564DOI 10.2977/PRIMS/1195176449