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International Journal of Algebra and Computation, 2010
For a finite semigroup S and pseudovariety V, (Y, T) is a V-stable pair of S iff Y ⊆ S, T ≤ S and for any relational morphism R : S ⇝ V with V ∈ V there exists a v ∈ V such that Y ⊆ R-1(v) and T ≤ R-1( Stab (v)). X ≤ S is stable if it is generated by an [Formula: see text]-chain {ai} with aiaj = ai for j < i. Given a relation R : S ⇝ A ∈ A (where A
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For a finite semigroup S and pseudovariety V, (Y, T) is a V-stable pair of S iff Y ⊆ S, T ≤ S and for any relational morphism R : S ⇝ V with V ∈ V there exists a v ∈ V such that Y ⊆ R-1(v) and T ≤ R-1( Stab (v)). X ≤ S is stable if it is generated by an [Formula: see text]-chain {ai} with aiaj = ai for j < i. Given a relation R : S ⇝ A ∈ A (where A
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Mathematical Logic Quarterly, 1991
The paper investigates definitions of k-tuples (k\(\geq 2)\) which are of the following form: \(=\{\{x_ 1\}\cup C_ 1,...,\{x_ k\}\cup C_ k\}\). A (rather artificial) definition adequate for any \(k\geq 2\) is given. However, if some natural constraints are satisfied then \(k=2\) and only the classical definitions of pairs by Hausdorff (1914), Wiener ...
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The paper investigates definitions of k-tuples (k\(\geq 2)\) which are of the following form: \(=\{\{x_ 1\}\cup C_ 1,...,\{x_ k\}\cup C_ k\}\). A (rather artificial) definition adequate for any \(k\geq 2\) is given. However, if some natural constraints are satisfied then \(k=2\) and only the classical definitions of pairs by Hausdorff (1914), Wiener ...
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Competence Assessments: To Pair or Not to Pair, That Is the Question
Journal of Continuing Education in the Health Professions, 2015Alison A, Heintz, Sara R, Fagerlie
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