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Article Dans Une Revue Algebra Universalis Année : 1995

Equational compactness of bi-frames and projection algebras

Résumé

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.
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Dates et versions

hal-00004209 , version 1 (10-02-2005)

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Friedrich Wehrung. Equational compactness of bi-frames and projection algebras. Algebra Universalis, 1995, 33 (4), pp.478-515. ⟨10.1007/BF01225471⟩. ⟨hal-00004209⟩
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