The semantical hyperunification problem

Klaus Denecke; Jörg Koppitz; Shelly Wismath

Displaying similar documents to “The semantical hyperunification problem”

Generalized deductive systems in subregular varieties

Ivan Chajda (2003)

Mathematica Bohemica

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An algebra $𝒜 = (A, F)$ is subregular alias regular with respect to a unary term function $g$ if for each $Θ, Φ \in Con 𝒜$ we have $Θ = Φ$ whenever ${[g (a)]}_{Θ} = {[g (a)]}_{Φ}$ for each $a \in A$ . We borrow the concept of a deductive system from logic to modify it for subregular algebras. Using it we show that a subset $C \subseteq A$ is a class of some congruence on $Θ$ containing $g (a)$ if and only if $C$ is this generalized deductive system. This method is efficient (needs a finite number of steps).

On the structure of equationally complete varieties. I

Don Pigozzi (1981)

Colloquium Mathematicae

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A note on dual discriminator varieties.

Ramalho, Margarita (2001)

Portugaliae Mathematica. Nova Série

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Notes on congruence implication

Gábor Czédli (1991)

Archivum Mathematicum

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Complexity of hypersubstitutions and lattices of varieties

Thawhat Changphas, Klaus Denecke (2003)

Discussiones Mathematicae - General Algebra and Applications

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Hypersubstitutions are mappings which map operation symbols to terms. The set of all hypersubstitutions of a given type forms a monoid with respect to the composition of operations. Together with a second binary operation, to be written as addition, the set of all hypersubstitutions of a given type forms a left-seminearring. Monoids and left-seminearrings of hypersubstitutions can be used to describe complete sublattices of the lattice of all varieties of algebras of a given type. The...

Diamond identities for relative congruences

Gábor Czédli (1995)

Archivum Mathematicum

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For a class $K$ of structures and $A \in K$ let ${C o n}^{*} (A)$ resp. ${C o n}^{K} (A)$ denote the lattices of $*$ -congruences resp. $K$ -congruences of $A$ , cf. Weaver [25]. Let ${C o n}^{*} (K) : = I {{C o n}^{*} (A) : A \in K}$ where $I$ is the operator of forming isomorphic copies, and ${C o n}^{r} (K) : = I {{C o n}^{K} (A) : A \in K}$ . For an ordered algebra $A$ the lattice of order congruences of $A$ is denoted by ${C o n}^{<} (A)$ , and let ${C o n}^{<} (K) : = I {{C o n}^{<} (A) : A \in K}$ if $K$ is a class of ordered algebras. The operators of forming subdirect squares and direct products are denoted by $Q^{s}$ and $P$ , respectively. Let $λ$ be a lattice identity and let $Σ$ be a set of lattice identities....