Abstract
If \( {\mathbb {V}} \) is a subvariety of \( {\mathbb {BL}} \) generated by a class of standard BL-algebras, then \( {\mathbb {V}} \) is generated by a finite class of standard BL-algebras.
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References
Aglianò, P., Ferreirim, I.M.A., Montagna, F.: Basic hoops: an algebraic study of continuous t-norms. Stud. Log. 87(1), 73–98 (2007)
Aglianò, P., Montagna, F.: Varieties of BL-algebras I: General properties. J. Pure Appl. Algebra 181(2–3), 105–129 (2003)
Argyros, S.A., Todorcevic, S.: Ramsey Methods in Analysis. Birkhäuser Verlag, Basel-Boston-Berlin (2005)
Baaz, M., Hájek, P., Montagna, F., Veith, H.: Complexity of t-tautologies. Ann. Pure Appl. Logic 113(1–3), 3–11 (2002)
Busaniche, M., Montagna, F.: Hájek’s logic BL and BL-algebras, Chapter V. In: Cintula, P., Hájek, P., Noguera, C. (eds.) Handbook of Mathematical Fuzzy Logic, vol. 1. Studies in Logic, vol. 37. College Publications (2011)
Cignoli, R., Esteva, F., Godo, L., Torrens, A.: Basic fuzzy logic is the logic of continuous t-norms and their residua. Soft Comput. 4(2), 106–112 (2000)
Esteva, F., Godo, L., Montagna, F.: Equational characterization of subvarieties of BL-algebras generated by t-norm algebras. Stud. Log. 76(2), 161–200 (2004)
Ferreirim, I.M.A.: On varieties and quasivarieties of hoops and their reducts. PhD thesis, University of Illinois at Chicago, Chicago (1992)
Galatos, N.: Equational bases for joins of residuated-lattice varieties. Stud. Log. 76(2), 227–240 (2004)
Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated lattices: an algebraic glimpse at substructural logics. In: Studies in Logic and the Foundations of Mathematics, vol. 151. Elsevier, Amsterdam (2007)
Hájek, P.: Basic fuzzy logic and BL-algebras. Soft Comput. 2(3), 124–128 (1998)
Hájek, P.: Metamathematics of fuzzy logic. In: Trends in Logic, vol. 4. Kluwer, Dordrecht (1998)
Haniková, Z.: A note on the complexity of propositional tautologies of individual t-algebras. Neural Netw. World 12, 453–460 (2002)
Horčík, R., Terui, K.: Disjunction property and complexity of substructural logics. Theor. Comp. Sci. 412(31), 3992–4006 (2011)
Mostert, P.S., Shields, A.L.: On the structure of semigroups on a compact manifold with boundary. Ann. Math. Second Series 65, 117–143 (1957)
Ono, H.: Logic without the contraction rule and residuated lattices. Aust. J. Logic (8), 50–81 (2010)
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Haniková, Z. Varieties Generated by Standard BL-Algebras. Order 31, 15–33 (2014). https://doi.org/10.1007/s11083-013-9285-5
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DOI: https://doi.org/10.1007/s11083-013-9285-5