Skip to main content
SpringerLink
Log in

Free Q-distributive lattices

  • Published:
Studia Logica Aims and scope Submit manuscript

Abstract

The dual spaces of the free distributive lattices with a quantifier are constructed, generalizing Halmos' construction of the dual spaces of free monadic Boolean algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Adams, M. E. and W. Dziobiak, 1994, ‘Quasivarieties of distributive lattices with a quantifier’, Discrete Math., 135, 15–28.

    Google Scholar 

  2. Cignoli, R., 1991, ‘Quantifiers on distributive lattices’, Discrete Math. 96, 183–197.

    Google Scholar 

  3. Cignoli, R., S. LaFalce, A. Petrovich, 1991, ‘Remarks on Priestley duality for distributive lattices’, Order 8, 299–315.

    Google Scholar 

  4. Halmos, P. R., 1955, ‘Algebraic logic. I. Monadic Boolean algebras’, Compositio Math. 12, 217–249. Reproduced in [Chapter II, Halmos 1962].

    Google Scholar 

  5. Halmos, P. R., 1959, ‘Free monadic algebras’, Proc. Amer. Math.Soc. 10, 219–227. Reproduced in [Chapter V, Halmos 1962].

    Google Scholar 

  6. Halmos, P. R., 1962, Algebraic logic, Chelsea, New York.

    Google Scholar 

  7. Henkin, L., J. D. Monk, A. Tarski, 1985, Cylindric Algebras. Part II, North-Holland, Amsterdam.

    Google Scholar 

  8. Priestley, H. A., 1970, ‘Representation of distributive lattices by means of ordered Stone spaces’, Bull. London Math. Soc. 2, 186–190.

    Google Scholar 

  9. Priestley, H. A., 1972, ‘Ordered topological spaces and the representation of distibutive lattices’, Proc. London Math. Soc. 4, (3), 507–530.

    Google Scholar 

  10. Priestley, H. A., 1984, ‘Ordered sets and duality for distributive lattices’, Ann. Discrete Math. 23, North-Holland, Amsterdam, 39–60.

  11. Priestley, H. A., 1991, ‘Natural dualities for varieties of distributive lattices with a quantifier’, in: C. Rauszer (ed.), Proc. 38th. Banach Centre Semester on Algebraic Methods in Logic and their Computer Science Applications, Banach Centre Publications, 28, Warsaw.

  12. Servi, M., 1979, ‘Un'assiomatizzazione dei reticoli esistenziali’, Boll. Un. Mat. Ital. 16 (5), 298–301.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática, Facultad de Ciencias Exactas Y Naturales, Universidad de Buenos Aires. Ciudad Universitaria, 1428, Buenos Aires, Argentina

    Roberto Cignoli

Authors
  1. Roberto Cignoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cignoli, R. Free Q-distributive lattices. Stud Logica 56, 23–29 (1996). https://doi.org/10.1007/BF00370139

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00370139

Key words

Search

Navigation