Quasivarieties of pseudocomplemented semilattices

M. Adams; Wiesław Dziobiak; Matthew Gould; Jürg Schmid

Fundamenta Mathematicae (1995)

  • Volume: 146, Issue: 3, page 295-312
  • ISSN: 0016-2736

Abstract

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Two properties of the lattice of quasivarieties of pseudocomplemented semilattices are established, namely, in the quasivariety generated by the 3-element chain, there is a sublattice freely generated by ω elements and there are 2 ω quasivarieties.

How to cite

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Adams, M., et al. "Quasivarieties of pseudocomplemented semilattices." Fundamenta Mathematicae 146.3 (1995): 295-312. <http://eudml.org/doc/212068>.

@article{Adams1995,
abstract = {Two properties of the lattice of quasivarieties of pseudocomplemented semilattices are established, namely, in the quasivariety generated by the 3-element chain, there is a sublattice freely generated by ω elements and there are $2^ω$ quasivarieties.},
author = {Adams, M., Dziobiak, Wiesław, Gould, Matthew, Schmid, Jürg},
journal = {Fundamenta Mathematicae},
keywords = {lattice of quasivarieties; pseudocomplemented semilattice; quasivariety},
language = {eng},
number = {3},
pages = {295-312},
title = {Quasivarieties of pseudocomplemented semilattices},
url = {http://eudml.org/doc/212068},
volume = {146},
year = {1995},
}

TY - JOUR
AU - Adams, M.
AU - Dziobiak, Wiesław
AU - Gould, Matthew
AU - Schmid, Jürg
TI - Quasivarieties of pseudocomplemented semilattices
JO - Fundamenta Mathematicae
PY - 1995
VL - 146
IS - 3
SP - 295
EP - 312
AB - Two properties of the lattice of quasivarieties of pseudocomplemented semilattices are established, namely, in the quasivariety generated by the 3-element chain, there is a sublattice freely generated by ω elements and there are $2^ω$ quasivarieties.
LA - eng
KW - lattice of quasivarieties; pseudocomplemented semilattice; quasivariety
UR - http://eudml.org/doc/212068
ER -

References

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  1. [1] M. E. Adams, Implicational classes of pseudocomplemented distributive lattices, J. London Math. Soc. 13 (1976), 381-384. Zbl0358.06025
  2. [2] M. E. Adams and W. Dziobiak, Q-universal quasivarieties of algebras, Proc. Amer. Math. Soc. 120 (1994), 1053-1059. Zbl0810.08007
  3. [3] M. E. Adams and W. Dziobiak, Lattices of quasivarieties of 3-element algebras, J. Algebra 166 (1994), 181-210. 
  4. [4] M. E. Adams and M. Gould, A construction for pseudocomplemented semilattices and two applications, Proc. Amer. Math. Soc. 106 (1989), 899-905. Zbl0695.06004
  5. [5] S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer, New York, 1981. 
  6. [6] W. Dziobiak, On subquasivariety lattices of some varieties related with distributive p-algebras, Algebra Universalis 21 (1985), 62-67. Zbl0589.08007
  7. [7] G. Grätzer, General Lattice Theory, Birkhäuser, Basel, 1978. Zbl0436.06001
  8. [8] G. T. Jones, Pseudocomplemented semilattices, Ph.D. dissertation, U.C.L.A., 1972. 
  9. [9] A. I. Mal'cev, On certain frontier questions in algebra and mathematical logic, Proc. Internat. Congr. of Mathematicians, Moscow 1966, Mir, 1968, 217-231 (in Russian). 
  10. [10] A. I. Mal'cev, Algebraic Systems, Grundlehren Math. Wiss. 192, Springer, New York, 1973. 
  11. [11] H. P. Sankappanavar, Remarks on subdirectly irreducible pseudocomplemented semi-lattices and distributive pseudocomplemented lattices, Math. Japon. 25 (1980), 519-521. Zbl0472.06009
  12. [12] M. V. Sapir, The lattice of quasivarieties of semigroups, Algebra Universalis 21 (1985), 172-180. Zbl0599.08014
  13. [13] J. Schmid, Lee classes and sentences for pseudocomplemented semilattices, ibid. 25 (1988), 223-232. Zbl0619.06005
  14. [14] J. Schmid, On amalgamation classes of pseudocomplemented semilattices, ibid. 29 (1992), 402-418. Zbl0783.06003
  15. [15] A. Shafaat, On implicational completeness, Canad. J. Math. 26 (1974), 761-768. Zbl0295.08003
  16. [16] M. P. Tropin, An embedding of a free lattice into the lattice of quasivarieties of distributive lattices with pseudocomplementation, Algebra i Logika 22 (1983), 159-167 (in Russian). 
  17. [17] A. Wroński, The number of quasivarieties of distributive lattices with pseudocomplementation, Polish Acad. Sci. Inst. Philos. Sociol. Sect. Logic 5 (1976), 115-121. Zbl0388.06009

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