The present work describes elementary submodels of a theory and establishes omega-stability in the solvable Baumslag-Solitar group, suggesting robust structural properties.
The author previously defined the divisible completion of the solvable Baumslag–Solitar group, described the groups elementarily equivalent to it, constructed an axiomatization of the corresponding theory, and proved its decidability. In the present work, elementary submodels of models of this theory are described, and ω -stability is established.
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N. S. Romanovskii (2026) studied this question.
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