Completion of the Solvable Baumslag–Solitar Group. Stability

Key Points

• This work focuses on describing elementary submodels and proving the omega-stability of the divisible completion of the solvable Baumslag-Solitar group.
• Defined the divisible completion of the solvable Baumslag-Solitar group
• Described groups elementarily equivalent to the completion
• Constructed an axiomatization of the theory
• Proved the decidability of the theory
• Established properties of elementary submodels.
• Described elementary submodels of the divisible completion
• Established the omega-stability of the completion
• Showed that the theory has robust structural properties.

Abstract