Skip to main content
SpringerLink
Log in

Density and closure in implicative semi-lattices

  • Published:
algebra universalis Aims and scope Submit manuscript

Abstract

The concept of dense and closed elements is extended to arbitrary implicative semi-lattices. It is shown that the Glivenko theorem does not hold in general. However every implicative semi-lattice can be embedded in a dense-closed preserving manner in a bounded implicative semi-lattice in which, of course, the Glivenko theorem holds.

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. Garrett Birkhoff,Lattice Theory, 3rd edition, J. Amer. Math. Soc., Providence, R. I., 1967.

    Google Scholar 

  2. W. C. Nemitz,Implicative semi-lattices, Trans. Amer. Math. Soc.117 (1965), 128–142.

    Article  MATH  MathSciNet  Google Scholar 

  3. W. C. Nemitz,On the lattice of filters of an implicative semi-lattice, J. Math. Mech.28 (1969), 683–688.

    MathSciNet  Google Scholar 

  4. W. C. Nemitz,Implicative homomorphisms with finite ranges, Proc. Amer. Math. Soc.33 (1972), 319–322.

    Article  MATH  MathSciNet  Google Scholar 

  5. W. C. Nemitz and T. Whaley,Varieties of implicative semi-lattices, Pacific J. Math.37 (1971), 759–769.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Southwestern at Memphis, Memphis, Tennessee, USA

    J. Eastham & W. Nemitz

Authors
  1. J. Eastham
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. W. Nemitz
    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

Eastham, J., Nemitz, W. Density and closure in implicative semi-lattices. Algebra Universalis 5, 1–7 (1975). https://doi.org/10.1007/BF02485225

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02485225

Keywords

Search

Navigation