Algebras of implication and semi-lattices

James C. Abbott

Displaying similar documents to “Algebras of implication and semi-lattices”

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Cecylia Rauszer (1974)

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Cecylia Rauszer (1977)

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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.

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In a previous paper, we introduced the notion of Boolean-like algebra as a generalisation of Boolean algebras to an arbitrary similarity type. In a nutshell, a double-pointed algebra $𝐀$ with constants $0, 1$ is Boolean-like in case for all $a \in A$ the congruences $θ (a, 0)$ and $θ (a, 1)$ are complementary factor congruences of $𝐀$ . We also introduced the weaker notion of semi-Boolean-like algebra, showing that it retained some of the strong algebraic properties characterising Boolean algebras. In this paper, we continue...

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Roman Sikorski (1963)

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