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.
ملخص البحث
قسم البحث
مجلة البحث
Communications in Algebra
المشارك في البحث
الناشر
Taylor & Francis Group
تصنيف البحث
1
عدد البحث
Volume 43, Issue 6
موقع البحث
http://www.tandfonline.com/doi/abs/10.1080/00927872.2013.876236#.VY3ra2VbfFw
سنة البحث
2015
صفحات البحث
2425-2436