The definable content of homological invariants I: ExtExt and lim1lim¹

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Definable invariants enhance classical functors, increasing their power for classification purposes.
The definable Ext is a fully faithful contravariant functor for finite-rank torsion-free abelian groups, unlike its classical counterpart.
The study introduces an Ulam stability framework, contributing to several rigidity results for non-Archimedean abelian groups with Polish covers. The results also address unknowns regarding quotients of p-adic groups, advancing understanding in the field.

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The paper demonstrates enriched invariants from classical homological algebra using Polish covers, suggesting stronger classification methods.

Bergfalk et al. (2024) studied this question.

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The paper demonstrates enriched invariants from classical homological algebra using Polish covers, suggesting stronger classification methods.