Displaying similar documents to “A common approach to directoids with an antitone involution and D-quasirings”

Two constructions of De Morgan algebras and De Morgan quasirings

Ivan Chajda, Günther Eigenthaler (2009)

Discussiones Mathematicae - General Algebra and Applications

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De Morgan quasirings are connected to De Morgan algebras in the same way as Boolean rings are connected to Boolean algebras. The aim of the paper is to establish a common axiom system for both De Morgan quasirings and De Morgan algebras and to show how an interval of a De Morgan algebra (or De Morgan quasiring) can be viewed as a De Morgan algebra (or De Morgan quasiring, respectively).

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.

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.

Topological representation for monadic implication algebras

Abad Manuel, Cimadamore Cecilia, Díaz Varela José (2009)

Open Mathematics

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In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.