B-separating algebras
A universal algebra A is said to be B-separating if any isomorphism of its Boolean powers \(A[B_ 1]\) and \(A[B_ 2]\) implies \(B_ 1\cong B_ 2\). In this paper some problems of \textit{S. Burris} [Algebra Univers. 5, 341-360 (1975; Zbl 0328.08003)] are solved. In particular the following results are proved: 1) No Abelian group is B-separating; 2) If A is a finite B-separating algebra and A[B] is equationally compact then B is complete; 3) (GCH) If A[B] is k-saturated (k\(\geq \omega)\) then B is k- saturated; 4) If A is a finite B-separating algebra then \(A[B_ 1]\equiv A[B_ 2]\Rightarrow B_ 1\equiv B_ 2\) (elementary equivalence).
scientific article; zbMATH DE number 4010584