Abstract elementary classes of R-modules with pure submodules are not always stable, but tame ones are almost stable and those with amalgamation are stable assuming a strongly compact cardinal.
Mazari-Armida.Some stable non-elementary classes of modules
2 Pith papers cite this work. Polarity classification is still indexing.
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math.LO 2years
2025 2representative citing papers
Introduces CP(K, *) in AECs to derive non-axiomatizability of uncountably categorical classes in L_{∞,ω1} (ZFC) and L_{∞,∞} (V=L) for free products of cyclic groups, torsion-free abelian groups, Steiner systems, and n-gons.
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On the problem of stability of abstract elementary classes of modules
Abstract elementary classes of R-modules with pure submodules are not always stable, but tame ones are almost stable and those with amalgamation are stable assuming a strongly compact cardinal.
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A New Construction Principle
Introduces CP(K, *) in AECs to derive non-axiomatizability of uncountably categorical classes in L_{∞,ω1} (ZFC) and L_{∞,∞} (V=L) for free products of cyclic groups, torsion-free abelian groups, Steiner systems, and n-gons.