Skip to main content
SpringerLink
Log in

The FEP for some varieties of fully distributive knotted residuated lattices

  • Published:
Algebra universalis Aims and scope Submit manuscript

Abstract

We prove the finite embeddability property for a wide range of varieties of fully distributive residuated lattices and FL-algebras. Part of the axiomatization is assumed to be a knotted inequality and some appropriate generalization of commutativity. The construction is based on distributive residuated frames and extends to subvarieties axiomatized by any division-free equation.

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. Blok W.J., van Alten C.J.: On the finite embeddability property for residuated lattices, pocrims and BCK-algebras. Rep. Math. Logic 34, 159–165 (2000)

    MATH  MathSciNet  Google Scholar 

  2. Blok W.J., van Alten C.J.: The finite embeddability property for residuated lattices, pocrims and BCK-algebras. Algebra Universalis 48, 253–271 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  3. Blok W.J., van Alten C.J.: On the finite embeddability property for residuated ordered groupoids. Trans. Amer. Math. Soc. 357, 4141–4157 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  4. Cardona R., Galatos N.: The finite embeddability property for noncommutative knotted extensions of RL. Internat. J. Algebra Comput. 25, 349–379 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  5. Galatos N., Horčík R.: Cayley’s and Holland’s theorems for idempotent semirings and their applications to residuated lattices. Semigroup Forum 87, 569–589 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  6. Galatos N., Jipsen P.: Residuated frames with applications to decidability. Trans. Amer. Math. Soc. 365, 1219–1249 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  7. Galatos, N., Jipsen, P.: Distributive residuated frames and generalized bunched implication algebras. Algebra Universalis (in press)

  8. Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated Lattices: An Algebraic Glimpse at Substructural Logics. Studies in Logic and the Foundations of Mathematics, vol 151. Elsevier, Amsterdam (2007)

  9. Higman G.: Ordering by divisibility in abstract algebras. Proc. London Math. Soc. 3, 326–336 (1952)

    Article  MATH  MathSciNet  Google Scholar 

  10. Horčík R.: Word problem for knotted residuated lattices. J. Pure Appl. Algebra 219, 1548–1563 (2015)

    Article  MATH  MathSciNet  Google Scholar 

  11. Jančar P.: A note on well quasi-orderings for powersets. Inform. Process. Lett. 72, 155–160 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  12. Marcone A.: Fine analysis of the quasi-orderings on the power set. Order 18, 339–347 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  13. Milner, E.C.: Basic wqo- and bqo-theory. In: Graphs and order (Banff, Alta., 1984). NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 147, pp. 487–502. Reidel, Dordrecht (1985)

  14. Nash-Williams C.St.J.A.: On well-quasi-ordering finite trees. Proc. Cambridge Philos. Soc. 59, 833–835 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  15. Nash-Williams C.St.J.A.: On well-quasi-ordering infinite trees. Proc. Cambridge Philos. Soc. 61, 697–720 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  16. Rado R.: Partial well-ordering of sets of vectors. Mathematika 1, 89–95 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  17. van Alten C.J.: The finite model property for knotted extensions of propositional linear logic. J. Symbolic Logic 70, 84–98 (2005)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Escuela de Matemática, Universidad de El Salvador. Ciudad Universitaria, Final de Av. Mártires y Héroes del 30 julio, San Salvador, El Salvador

    Riquelmi Cardona

  2. Department of Mathematics, University of Denver, C.M. Knudson Hall, 2390 S. York St., Denver, CO, 80208, USA

    Nikolaos Galatos

Authors
  1. Riquelmi Cardona
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nikolaos Galatos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikolaos Galatos.

Additional information

Presented by J. Raftery.

The second author acknowledges the support of the grants Simons Foundation 245805 and FWF project START Y544-N23.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cardona, R., Galatos, N. The FEP for some varieties of fully distributive knotted residuated lattices. Algebra Univers. 78, 363–376 (2017). https://doi.org/10.1007/s00012-017-0466-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00012-017-0466-8

2010 Mathematics Subject Classification

Key words and phrases

Search

Navigation