Studia Logica

, Volume 54, Issue 3, pp 371–389 | Cite as

Joins of minimal quasivarieties

  • M. E. Adams
  • W. Dziobiak


LetL(K) denote the lattice (ordered by inclusion) of quasivarieties contained in a quasivarietyK and letD2 denote the variety of distributive (0, 1)-lattices with 2 additional nullary operations. In the present paperL(D2) is described. As a consequence, ifM+N stands for the lattice join of the quasivarietiesM andN, then minimal quasivarietiesV0,V1, andV2 are given each of which is generated by a 2-element algebra and such that the latticeL(V0+V1), though infinite, still admits an easy and nice description (see Figure 2) while the latticeL(V0+V1+V2), because of its intricate inner structure, does not. In particular, it is shown thatL(V0+V1+V2) contains as a sublattice the ideal lattice of a free lattice with ω free generators. Each of the quasivarietiesV0,V1, andV2 is generated by a 2-element algebra inD2.

Key words

Quasivariety lattice of quasivarieties distributive (0, 1)-lattice nullary operations free lattice Priestley space graph 

1991 Mathematics Subject Classification

Primary: 06D99, 08C15 Secondary: 06B25 


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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • M. E. Adams
    • 1
  • W. Dziobiak
    • 2
  1. 1.Department of Mathematics and Computer ScienceState University of New YorkNew PaltzUSA
  2. 2.Department of MathematicsUniversity of Puerto RicoMayaguezUSA

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