Completion of the Solvable Baumslag–Solitar group. Elementary Theory
摘要
For the solvable Baumslag–Solitar group BS(1, n) (n > 1), we define the divisible completion BSd(1, n). We describe groups that are elementarily equivalent to the group BSd(1, n), find the axiomatics of the theory of the group BSd(1, n), and prove the decidability of this theory.