Varieties of Algebras without the Amalgamation Property |
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Authors: | Basim Samir |
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Affiliation: | 1. Department of Mathematics, Faculty of Science , Assiut University , Assiut , Egypt basim200@yahoo.com |
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Abstract: | Let α be an ordinal and κ be a cardinal, both infinite, such that κ ≤ |α|. For τ ∈αα, let sup(τ) = {i ∈ α: τ(i) ≠ i}. Let G κ = {τ ∈αα: |sup(τ)| < κ}. We consider variants of polyadic equality algebras by taking cylindrifications on Γ ? α, |Γ| < κ and substitutions restricted to G κ. Such algebras are also enriched with generalized diagonal elements. We show that for any variety V containing the class of representable algebas and satisfying a finite schema of equations, V fails to have the amalgamation property. In particular, many varieties of Halmos’ quasi-polyadic equality algebras and Lucas’ extended cylindric algebras (including that of the representable algebras) fail to have the amalgamation property. |
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Keywords: | Algebraic logic Amalgamation Polyadic algebras |
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