Abstract
We find some links between Σ-reducibility and T-reducibility. We prove that (1) if a quasirigid model is strongly Σ-definable in a hereditarily finite admissible set over a locally constructivizable B-system, then it is constructivizable; (2) every abelian p-group and every Ershov algebra is locally constructivizable; (3) if an antisymmetric connected model is Σ-definable in a hereditarily finite admissible set over a countable Ershov algebra then it is constructivizable.
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