Natural dualities for varieties of distributive lattices with a quantifier

H. Priestley

Banach Center Publications (1993)

  • Volume: 28, Issue: 1, page 291-310
  • ISSN: 0137-6934

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Priestley, H.. "Natural dualities for varieties of distributive lattices with a quantifier." Banach Center Publications 28.1 (1993): 291-310. <http://eudml.org/doc/262789>.

@article{Priestley1993,
author = {Priestley, H.},
journal = {Banach Center Publications},
keywords = {natural duality; quantifier; free algebra; distributive lattices with a quantifier; category; variety of - distributive lattices; duality based on hom-functors; schizophrenic object; natural dualities; free algebras},
language = {eng},
number = {1},
pages = {291-310},
title = {Natural dualities for varieties of distributive lattices with a quantifier},
url = {http://eudml.org/doc/262789},
volume = {28},
year = {1993},
}

TY - JOUR
AU - Priestley, H.
TI - Natural dualities for varieties of distributive lattices with a quantifier
JO - Banach Center Publications
PY - 1993
VL - 28
IS - 1
SP - 291
EP - 310
LA - eng
KW - natural duality; quantifier; free algebra; distributive lattices with a quantifier; category; variety of - distributive lattices; duality based on hom-functors; schizophrenic object; natural dualities; free algebras
UR - http://eudml.org/doc/262789
ER -

References

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  1. [1] M. E. Adams and H. A. Priestley, Equational bases for varieties of Ockham algebras, Algebra Universalis, to appear. Zbl0811.06011
  2. [2] G. E. Andrews, The Theory of Partitions, Encyclopedia Math. Appl. 2, Addison-Wesley, Reading, MA, 1976. 
  3. [3] R. Cignoli, Quantifiers on distributive lattices, Discrete Math. 96 (1991), 188-197. Zbl0753.06012
  4. [4] R. Cignoli, Free Q-distributive lattices, manuscript. 
  5. [5] R. Cignoli, S. Lafalce and A. Petrovich, Remarks on Priestley duality for distributive lattices, Order 8 (1991), 299-315. Zbl0754.06006
  6. [6] D. M. Clark and P. H. Krauss, On topological quasi-varieties, Acta Sci. Math. (Szeged) 47 (1983), 3-39. Zbl0561.08005
  7. [7] B. A. Davey, Duality theory on ten dollars a day, in: Proc. SMS Summer School on Algebras and Orders, Montréal 1991, NATO Adv. Study Inst. Ser. 389, 71-111. Zbl0793.08001
  8. [8] B. A. Davey and M. S. Goldberg, The free p-algebra generated by a distributive lattice, Algebra Universalis 11 (1980), 90-100. Zbl0386.06003
  9. [9] B. A. Davey and H. A. Priestley, Generalised piggyback dualities and applications to Ockham algebras, Houston J. Math. 13 (1987), 151-197. Zbl0692.08012
  10. [10] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, Cambridge Univ. Press, Cambridge 1990. Zbl0701.06001
  11. [11] B. A. Davey and H. A. Priestley, Partition-induced natural dualities for varieties of pseudocomplemented distributive lattices, Discrete Math. 113 (1993), 41-58. Zbl0781.06008
  12. [12] B. A. Davey and H. A. Priestley, Optimal natural dualities, Trans. Amer. Math. Soc., to appear. Zbl0804.06014
  13. [13] B. A. Davey and H. A. Priestley, Optimal dualities for varieties of Heyting algebras, preprint. Zbl0854.06011
  14. [14] B. A. Davey and H. Werner, Dualities and equivalences for varieties of algebras, in: Contributions to Lattice Theory (Szeged 1980), A. P. Huhn and E. T. Schmidt (eds.), Colloq. Math. Soc. János Bolyai 33, North-Holland, Amsterdam 1983, 101-275. 
  15. [15] B. A. Davey and H. Werner, Piggyback dualities, in: Lectures in Universal Algebra (Szeged 1983), L. Szabó and A. Szendrei (eds.), Colloq. Math. Soc. János Bolyai 43, North-Holland, Amsterdam 1986, 61-83. 
  16. [16] B. A. Davey and H. Werner, Piggyback-Dualitäten, Bull. Austral. Math. Soc. 32 (1985), 1-32. 
  17. [17] R. Goldblatt, Varieties of complex algebras, Ann. Pure Appl. Logic 44 (1990), 173-242. Zbl0722.08005
  18. [18] P. R. Halmos, Algebraic logic I: monadic algebras, Compositio Math. 12 (1955), 217-249; reproduced in [19]. Zbl0087.24505
  19. [19] P. R. Halmos, Algebraic Logic, Chelsea, New York 1962. 
  20. [20] G. Hansoul, A duality for Boolean algebras with operators, Algebra Universalis 17 (1983), 34-49. 
  21. [21] H. A. Priestley, Ordered sets and duality for distributive lattices, in: Orders, Descriptions and Roles, M. Pouzet and D. Richard (eds.), Ann. Discrete Math. 23, North-Holland, Amsterdam 1984, 39-60. 
  22. [22] H. A. Priestley, The determination of subvarieties of certain congruence-% distributive varieties, Algebra Universalis, to appear. Zbl0816.08008
  23. [23] H. A. Priestley, Natural dualities, in: Proc. Birkhoff Symposium 1991, K. Baker and R. Wille (eds.), to appear. 
  24. [24] H. A. Priestley and M. P. Ward, A multi-purpose backtracking algorithm, submitted. 

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