 |
|
|
|
| HAL : hal-00004209, version 1 |
| DOI : 10.1007/BF01225471 |
| Fiche détaillée |  Récupérer au format |
|
|
| Algebra Universalis 33, 4 (1995) 478-515 |
|
|
|
|
| Equational compactness of bi-frames and projection algebras |
|
|
| Friedrich Wehrung 1 |
|
|
| (1995) |
|
|
|
| We generalize D. Kelly's and K.A. Nauryzbaev's results of 1-variable and 2-variable equational compactness of complete distributive lattices satisfying the infinite distributive law and its dual ("bi-frames") to objects similar to monadic algebras (which we will call projection algebras). This will lead us to an example of bi-frame that is not 3-variable equationally compact, even for countable equation systems, thus solving a problem posed in 1978 by G. Grätzer. This example is realized as a certain complete sublattice of the complete Boolean algebra of regular open subsets of some Polish space. |
|
|
|
|
|
|
|
|
|
|
|
| 1 : | Laboratoire de Mathématiques Nicolas Oresme (LMNO) |
|
|
|
CNRS : UMR6139 – Université de Caen Basse-Normandie |
|
|
|
|
|
|
|
|
|
| Domaine | : | Mathématiques/Mathématiques générales |
|
|
| equational compactness – monadic algebra – bi-frames – partially ordered set – lower set – Polish space – regular open sets – Baire property |
|
|
|
| Liste des fichiers attachés à ce document : | |||||
|
|||||
|
|
|
| hal-00004209, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00004209 | |
| oai:hal.archives-ouvertes.fr:hal-00004209 | |
| Contributeur : Friedrich Wehrung | |
| Soumis le : Jeudi 10 Février 2005, 10:47:13 | |
| Dernière modification le : Vendredi 18 Mars 2011, 11:48:38 | |
