<p>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&#xa0;this theory are described, and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$ \omega $</EquationSource> </InlineEquation>-stability is established.</p>

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Completion of the Solvable Baumslag–Solitar Group. Stability

  • N. S. Romanovskii

摘要

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 $ \omega $ -stability is established.