| Title:
|
Transferral of entailment in duality theory II: strong dualisability (English) |
| Author:
|
Gouveia, Maria João |
| Author:
|
Haviar, Miroslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
2 |
| Year:
|
2011 |
| Pages:
|
401-417 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
natural duality |
| Keyword:
|
(strong) dualisability |
| Keyword:
|
entailment |
| MSC:
|
08A35 |
| MSC:
|
08C15 |
| MSC:
|
08C20 |
| idZBL:
|
Zbl 1249.08014 |
| idMR:
|
MR2905413 |
| DOI:
|
10.1007/s10587-011-0063-5 |
| . |
| Date available:
|
2011-06-06T10:31:43Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141543 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/141517 |
| . |
| Reference:
|
[1] Clark, D. M., Davey, B. A.: Natural Dualities for the Working Algebraist.Cambridge University Press, Cambridge (1998). Zbl 0910.08001, MR 1663208 |
| Reference:
|
[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. MR 1835800, 10.1007/PL00000344 |
| Reference:
|
[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 1814235 |
| Reference:
|
[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. Zbl 0845.08006, MR 1367197, 10.2307/2275875 |
| Reference:
|
[5] Davey, B. A., Haviar, M., Willard, R.: Structural entailment.Algebra Universalis 54 (2005), 397-416. Zbl 1090.08009, MR 2218853, 10.1007/s00012-005-1944-y |
| Reference:
|
[6] Davey, B. A., Willard, R.: The dualisability of a quasi-variety is independent of the generating algebra.Algebra Universalis 45 (2001), 103-106. Zbl 1039.08006, MR 1809859, 10.1007/s000120050204 |
| Reference:
|
[7] Gouveia, M. J., Haviar, M.: Transferral of entailment in duality theory: dualisability.Czech. Math. J. 61 (2011), 41-63. MR 2782758, 10.1007/s10587-011-0016-z |
| Reference:
|
[8] Hyndman, J. J.: Strong duality of finite algebras that generate the same quasivariety.Algebra Universalis 51 (2004), 29-34. Zbl 1092.08004, MR 2067149, 10.1007/s00012-004-1847-3 |
| Reference:
|
[9] Pitkethly, J. G., Davey, B. A.: Dualisability: Unary Algebras and Beyond.Springer (2005). Zbl 1085.08001, MR 2161626 |
| Reference:
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[10] Saramago, M.: Some remarks on dualisability and endodualisability.Algebra Universalis 43 (2000), 197-212. Zbl 1011.08003, MR 1773938, 10.1007/s000120050153 |
| Reference:
|
[11] Saramago, M. J., Priestley, H. A.: Optimal natural dualities: the structure of failsets.Internat. J. Algebra Comput. 12 (2002), 407-436. Zbl 1027.08006, MR 1910686, 10.1142/S0218196702000791 |
| Reference:
|
[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. |
| Reference:
|
[13] Zádori, L.: Natural duality via a finite set of relations.Bull. Austral. Math. Soc. 51 (1995), 469-478. MR 1331440, 10.1017/S0004972700014301 |
| . |
