Transferral of entailment in duality theory II: strong dualisability
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 401-417
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Results saying how to transfer the entailment in certain minimal and maximal ways and how to transfer strong dualisability between two different finite generators of a quasi-variety of algebras are presented. A new proof for a well-known result in the theory of natural dualities which says that strong dualisability of a quasi-variety is independent of the generating algebra is derived.
Results saying how to transfer the entailment in certain minimal and maximal ways and how to transfer strong dualisability between two different finite generators of a quasi-variety of algebras are presented. A new proof for a well-known result in the theory of natural dualities which says that strong dualisability of a quasi-variety is independent of the generating algebra is derived.
DOI : 10.1007/s10587-011-0063-5
Classification : 08A35, 08C15, 08C20
Keywords: natural duality; (strong) dualisability; entailment
@article{10_1007_s10587_011_0063_5,
     author = {Gouveia, Maria Jo\~ao and Haviar, Miroslav},
     title = {Transferral of entailment in duality theory {II:} strong dualisability},
     journal = {Czechoslovak Mathematical Journal},
     pages = {401--417},
     year = {2011},
     volume = {61},
     number = {2},
     doi = {10.1007/s10587-011-0063-5},
     mrnumber = {2905413},
     zbl = {1249.08014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0063-5/}
}
TY  - JOUR
AU  - Gouveia, Maria João
AU  - Haviar, Miroslav
TI  - Transferral of entailment in duality theory II: strong dualisability
JO  - Czechoslovak Mathematical Journal
PY  - 2011
SP  - 401
EP  - 417
VL  - 61
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0063-5/
DO  - 10.1007/s10587-011-0063-5
LA  - en
ID  - 10_1007_s10587_011_0063_5
ER  - 
%0 Journal Article
%A Gouveia, Maria João
%A Haviar, Miroslav
%T Transferral of entailment in duality theory II: strong dualisability
%J Czechoslovak Mathematical Journal
%D 2011
%P 401-417
%V 61
%N 2
%U http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0063-5/
%R 10.1007/s10587-011-0063-5
%G en
%F 10_1007_s10587_011_0063_5
Gouveia, Maria João; Haviar, Miroslav. Transferral of entailment in duality theory II: strong dualisability. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 401-417. doi: 10.1007/s10587-011-0063-5

[1] Clark, D. M., Davey, B. A.: Natural Dualities for the Working Algebraist. Cambridge University Press, Cambridge (1998). | MR | Zbl

[2] Clark, D. M., Idziak, P. M., Sabourin, L. R., Szabó, Cs., Willard, R.: Natural dualities for quasi-varieties generated by a finite commutative ring. Algebra Universalis 46 (2001), 285-320. | DOI | MR

[3] Davey, B. A., Haviar, M.: A schizophrenic operation which aids the efficient transfer of strong dualitites. Houston Math. J. 26 (2000), 215-222. | MR

[4] Davey, B. A., Haviar, M., Priestley, H. A.: The syntax and semantics of entailment in duality theory. J. Symbolic Logic 60 (1995), 1087-1114. | DOI | MR | Zbl

[5] Davey, B. A., Haviar, M., Willard, R.: Structural entailment. Algebra Universalis 54 (2005), 397-416. | DOI | MR | Zbl

[6] Davey, B. A., Willard, R.: The dualisability of a quasi-variety is independent of the generating algebra. Algebra Universalis 45 (2001), 103-106. | DOI | MR | Zbl

[7] Gouveia, M. J., Haviar, M.: Transferral of entailment in duality theory: dualisability. Czech. Math. J. 61 (2011), 41-63. | DOI | MR

[8] Hyndman, J. J.: Strong duality of finite algebras that generate the same quasivariety. Algebra Universalis 51 (2004), 29-34. | DOI | MR | Zbl

[9] Pitkethly, J. G., Davey, B. A.: Dualisability: Unary Algebras and Beyond. Springer (2005). | MR | Zbl

[10] Saramago, M.: Some remarks on dualisability and endodualisability. Algebra Universalis 43 (2000), 197-212. | DOI | MR | Zbl

[11] Saramago, M. J., Priestley, H. A.: Optimal natural dualities: the structure of failsets. Internat. J. Algebra Comput. 12 (2002), 407-436. | DOI | MR | Zbl

[12] Willard, R.: New tools for proving dualizability. Dualities, Interpretability and Ordered Structures (Lisbon, 1997). J. Vaz de Carvalho and I. Ferreirim Centro de Álgebra da Universidade de Lisboa (1999), 69-74.

[13] Zádori, L.: Natural duality via a finite set of relations. Bull. Austral. Math. Soc. 51 (1995), 469-478. | DOI | MR

Cité par Sources :