JournalsprimsVol. 23, No. 3pp. 559–564

Undecidability of Free Pseudo-Complemented Semilattlces

  • Pawel M. Idziak

    Jagiellonian University, Krakow, Poland
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Decision problem for the first order theory of free objects in equational classes of algebras was investigated for groups (Malcev [10]), semigroups (Quine [12]), commutative semigroups (Mostowski [11]), distributive lattices (Ershov [6]) and several varieties of rings (Lavrov [9]). Recently this question was solved for all varieties of Hilbert algebras and distributive pseudo-complemented lattices (see [7], [8]). 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. 559–564

DOI 10.2977/PRIMS/1195176449