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 ∈ Con 𝒜 we have Θ = Φ whenever [ g ( a ) ] Θ = [ g ( a ) ] Φ for each a ∈ 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 ⊆ 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).

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 ∈ 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 ∈ K } where I is the operator of forming isomorphic copies, and C o n r ( K ) : = I { C o n K ( A ) : A ∈ 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 ∈ 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....