Free Spectra of Equivalential Algebras with Conjunction on Dense Elements

Sławomir Przybyło; Katarzyna Słomczyńska

doi:10.18778/0138-0680.2024.08

Authors

Sławomir Przybyło University of the National Education Commission https://orcid.org/0000-0001-8413-6754
Katarzyna Słomczyńska University of the National Education Commission https://orcid.org/0000-0002-7957-2583

DOI:

https://doi.org/10.18778/0138-0680.2024.08

Keywords:

Fregean varieties, equivalential algebras, dense elements, free algebra, free spectra

Abstract

We construct free algebras in the variety generated by the equivalential algebra with conjunction on dense elements and compute the formula for the free spectrum of this variety. Moreover, we describe the decomposition of free algebras into directly indecomposable factors.

References

P. M. Idziak, K. Słomczyńska, Polynomially rich algebras, Journal of Pure and Applied Algebra, vol. 156(1) (2001), pp. 33–68, DOI: https://doi.org/10.1016/S0022-4049(99)00119-X.
Google Scholar DOI: https://doi.org/10.1016/S0022-4049(99)00119-X

J. K. Kabziński, A. Wroński, On equivalential algebras, [in:] Proceedings of the 1975 International Symposium on Multipe-Valued Logic, Indiana University, Bloomington, Indiana, IEEE Comput. Soc., Long Beach (1975), pp. 419–428.
Google Scholar

P. Köhler, Brouwerian semilattices, Transactions of the American Mathematical Society, vol. 268(1) (1981), pp. 103–126, DOI: https://doi.org/10.1090/S0002-9947-1981-0628448-3.
Google Scholar DOI: https://doi.org/10.2307/1998339

S. Przybyło, Equivalential algebras with conjunction on the regular elements, Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, vol. 20 (2021), pp. 63–75, DOI: https://doi.org/10.2478/aupcsm-2021-0005.
Google Scholar DOI: https://doi.org/10.2478/aupcsm-2021-0005

S. Przybyło, K. Słomczyńska, Equivalential algebras with conjunction on the regular elements, Bulletin of the Section of Logic, vol. 51(4) (2022), pp. 535–554, DOI: https://doi.org/doi.org/10.18778/0138-0680.2022.22.
Google Scholar DOI: https://doi.org/10.18778/0138-0680.2022.22

K. Słomczyńska, Free spectra of linear equivalential algebras, The Journal of Symbolic Logic, vol. 70(4) (2005), pp. 1341–1358, DOI: https://doi.org/10.2178/jsl/1129642128.
Google Scholar DOI: https://doi.org/10.2178/jsl/1129642128

K. Słomczyńska, Free equivalential algebras, Annals of Pure and Applied Logic, vol. 155(2) (2008), pp. 86–96, DOI: https://doi.org/10.1016/j.apal.2008.03.003.
Google Scholar DOI: https://doi.org/10.1016/j.apal.2008.03.003

K. Słomczyńska, The structure of completely meet irreducible congruences in strongly Fregean algebras, Algebra Universalis, vol. 83(31) (2022), DOI: https://doi.org/10.1007/s00012-022-00787-0.
Google Scholar DOI: https://doi.org/10.1007/s00012-022-00787-0

A. Wroński, On the free equivalential algebra with three generators, Bulletin of the Section of Logic, vol. 22 (1993), pp. 37–39.
Google Scholar