Displaying similar documents to “A Galois correspondence for boolean algebras”

Clausal relations and C-clones

Edith Vargas (2010)

Discussiones Mathematicae - General Algebra and Applications

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We introduce a special set of relations called clausal relations. We study a Galois connection Pol-CInv between the set of all finitary operations on a finite set D and the set of clausal relations, which is a restricted version of the Galois connection Pol-Inv. We define C-clones as the Galois closed sets of operations with respect to Pol-CInv and describe the lattice of all C-clones for the Boolean case D = {0,1}. Finally we prove certain results about C-clones over a larger set. ...

The elementary-equivalence classes of clopen algebras of P-spaces

Brian Wynne (2008)

Fundamenta Mathematicae

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Two Boolean algebras are elementarily equivalent if and only if they satisfy the same first-order statements in the language of Boolean algebras. We prove that every Boolean algebra is elementarily equivalent to the algebra of clopen subsets of a normal P-space.

On Marczewski-Burstin representable algebras

Marek Balcerzak, Artur Bartoszewicz, Piotr Koszmider (2004)

Colloquium Mathematicae

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We construct algebras of sets which are not MB-representable. The existence of such algebras was previously known under additional set-theoretic assumptions. On the other hand, we prove that every Boolean algebra is isomorphic to an MB-representable algebra of sets.