On invariants for 𝜔₁-separable groups

Abstract

We study the classification of <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="omega 1"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msub> <mml:mi>ω<!-- ω --></mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:annotation encoding="application/x-tex">{\omega _1}</mml:annotation> </mml:semantics> </mml:math> </inline-formula>-separable groups by using Ehrenfeucht-Fraïssé games and prove a strong classification result assuming PFA, and a strong non-structure theorem assuming <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="normal ♢"> <mml:semantics> <mml:mi mathvariant="normal">♢<!-- ♢ --></mml:mi> <mml:annotation encoding="application/x-tex">\diamondsuit</mml:annotation> </mml:semantics> </mml:math> </inline-formula>.

Locations

• Transactions of the American Mathematical Society - View - PDF