Free algebras in varieties of BL-algebras generated by a BL n-chain

Journal of the Australian Mathematical Society

Volumn 80, Issue 3, 2006, Pages 419-439

  Busaniche, Manuela ^a   Cignoli, Roberto ^a  

^a UNIVERSIDAD DE BUENOS AIRES   (Argentina)

Author keywords

BL algebras; Boolean products; Free algebras; Hoops; Moisil algebras; Residuated lattices

Indexed keywords

EID: 33746218946     PISSN: 14467887     EISSN: None     Source Type: Journal    
DOI: 10.1017/S1446788700014117     Document Type: Article

References (25)

1. P. Aglianò, I. M. A. Ferreirim and F. Montagna, 'Basic hoops: An algebraic study of continuous t-norms', manuscript.
2. P. Aglianò and F. Montagna, 'Varieties of BL-algebras I: General properties', J. Pure Appl. Algebra 181 (2003), 105-129.
3. K. Amer, 'Equationally complete classes of conmutative monoids with monus'. Algebra Universalis 18 (1984), 129-131.
4. R. Balbes and P. Dwinger, Distributive lattices (University of Missoury Press, Columbia, 1974).
5. D. Bigelow and S. Burris, 'Boolean algebras of factor congruences', Acta Sci. Math. (Szeged) 54 (1990), 11-20.
6. W. J. Block and I. M. A. Ferreirim, 'Hoops and their implicational reducts (Abstract)', in: Algebraic Methods in Logic and Computer Sciences, Banach Center Publications 28 (Polish Academy of Science, Warsaw, 1993) pp. 219-230.
7. _, 'On the structure of hoops'. Algebra Universalis 43 (2000), 233-257.
8. V. Boicescu, A. Filipoiu, G. Georgescu and S. Rudeanu, Lukasiewicz-Moisil algebras (Elsevier, Amsterdam, 1991).
9. S. Burris and H. P. Sankappanavar, A course in universal algebra (Springer, New York, 1981).
10. M. Busaniche, 'Free algebras in varieties of BL-algebras generated by a chain', Algebra Universalis 50 (2003), 259-277.
11. R. Cignoli, Moisil algebras, Notas de lógica matemática (Institute De Matemática, Universidad Nac. del Sur, Bahía Bianca, Argentina, 1970).
12. _, 'Some algebraic aspects of many-valued logics', in: Proceedings of the third Brazilian Conference on Mathematical Logic (Sociedade Brasileira de Lógica) (eds. A. I. Arruda, N. C. A. da Costa and A. M. Sette) (S̃o Paulo, 1980) pp. 49-69.
13. _, 'Proper n-valued łukasiewicz algebras as S-algebras of łukasiewicz n-valued propositional calculi', Studia Logica 41 (1982), 3-16.
14. R. Cignoli, M. I. D'Ottaviano and D. Mundici, Algebraic foundations of many-valued reasoning (Kluwer, Dordrecht, 2000).
15. R. Cignoli and A. Torrens, 'An algebraic analysis of product logic', Mult.-Valued Log. 5 (2000), 45-65.
16. _, 'Free cancelative hoops', Algebra Universalis 43 (2000), 213-216.
17. _, 'Free algebras in varieties of BL-algebras with a Boolean retract', Algebra Universalis 48 (2002), 55-79.
18. _, 'Hájek basic fuzzy logic and łukasiewicz infinite-valued logic', Arch. Math. Logic 42 (2003), 361-370.
19. P. Hájek, Metamathematics of fuzzy logic (Kluwer, Dordrecht, 1998).
20. A. Horn, 'Free L-algebras', J. Symbolic Logic 34 (1969), 475-80.
21. n-algebras and n-valued łukasiewicz-moisil algebras. Part I, Discrete Math. 181 (1998), 155-177.
22. R. McNaughton, 'A theorem about infinite-valued sentential logic', J. Symbolic Logic 16 (1951), 1-13.
23. A. Di Nola, G. Georgescu and L. Leustean, 'Boolean products of BL-algebras', J. Math. Anal. Appl. 251 (2000), 106-131.
24. A. J. Rodríguez and A. Torrens, 'Wajsberg algebras and post algebras'. Studio Logica 53 (1994), 1-19.
25. J. von Plato, 'Skolem's discovery of Gödel-Dummett logic', Studio Logica 73 (2003), 153-157.