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A topological shuttle between inequalities and pseudoinequalities

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Abstract

Topological procedures to relate pseudoinequalities that define a pseudovariety of ordered algebras with inequalities that ultimately define it, and vice-versa, are presented.

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References

  1. Almeida, J.: Finite Semigroups and Universal Algebra. Series in Algebra 3. World Scientific (1995). https://doi.org/10.1142/2481

  2. Banaschewski, B.: The Birkhoff theorem for varieties of finite algebras. Algebra Univers. 17(1), 360–368 (1983). https://doi.org/10.1007/BF01194543

    Article  MathSciNet  MATH  Google Scholar 

  3. Birkhoff, G.: On the structure of abstract algebras. Math. Proc. Cambridge Philos. Soc. 31(4), 433–454 (1935). https://doi.org/10.1017/S0305004100013463

    Article  MATH  Google Scholar 

  4. Bloom, S.L.: Varieties of ordered algebras. J. Comput. Syst. Sci. 13(2), 200–212 (1976). https://doi.org/10.1016/S0022-0000(76)80030-X

    Article  MathSciNet  MATH  Google Scholar 

  5. Colcombet, T.: Regular cost functions, Part I: Logic and algebra over words. Log. Methods Comput. Sci. 9(3), 1–47 (2013). https://doi.org/10.2168/LMCS-9(3:3)2013

    Article  MathSciNet  MATH  Google Scholar 

  6. Eilenberg, S.: Automata, Languages, and Machines. Academic Press, Cambridge (1974)

    MATH  Google Scholar 

  7. Eilenberg, S., Schützenberger, M.P.: On pseudovarieties. Adv. in Math. 19(3), 413–418 (1976). https://doi.org/10.1016/0001-8708(76)90029-3

    Article  MathSciNet  MATH  Google Scholar 

  8. Fernandes, B.H.: Álgebras de estabilização. Master’s thesis, Faculdade de Ciências, Universidade de Lisboa (2018). http://hdl.handle.net/10451/34633

  9. Higgins, P.M.: An algebraic proof that pseudovarieties are defined by pseudoidentities. Algebra Univers. 27(4), 597–599 (1990). https://doi.org/10.1007/BF01189004

    Article  MathSciNet  MATH  Google Scholar 

  10. Molchanov, V.: Nonstandard characterization of pseudovarieties. Algebra Univers. 33(4), 533–547 (1995). https://doi.org/10.1007/BF01225473

    Article  MathSciNet  MATH  Google Scholar 

  11. Pin, J.É., Weil, P.: A Reiterman theorem for pseudovarieties of finite first-order structures. Algebra Univers. 35(4), 577–595 (1996). https://doi.org/10.1007/BF01243597

    Article  MathSciNet  MATH  Google Scholar 

  12. Reiterman, J.: The Birkhoff theorem for finite algebras. Algebra Univers. 14(1), 1–10 (1982). https://doi.org/10.1007/BF02483902

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

This project was partially supported by Fundação para a Ciência e a Tecnologia, FCT, under the Projects UIDB/04621/2020, UIDP/04621/2020 and PTDC/MAT-PUR/31174/2017, within the activities of Centro de Matemática Computacional e Estocástica, CEMAT, and Departamento de Matemática da Faculdade de Ciências da Universidade de Lisboa. The authors would like to thank Mário J. J. Branco for the pertinent discussions and suggestions.

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Authors and Affiliations

  1. Department of Mathematics, KTH Royal Institute of Technology, 114 28, Stockholm, Sweden

    Bernardo H. Fernandes

  2. Universidade de Lisboa, Faculdade de Ciências, Departamento de Matemática, 1749-016, Lisboa, Portugal

    Gracinda M. S. Gomes

Authors
  1. Bernardo H. Fernandes
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  2. Gracinda M. S. Gomes
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Correspondence to Gracinda M. S. Gomes.

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Communicated by Jorge Almeida.

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Fernandes, B.H., Gomes, G.M.S. A topological shuttle between inequalities and pseudoinequalities. Semigroup Forum 102, 916–924 (2021). https://doi.org/10.1007/s00233-021-10167-0

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