We prove that the set M of propositions independent of all levels of a transfinite hierarchy of reflective extensions of Peano arithmetic is Π₁¹-complete. The hierarchy is constructed via a deconstruction operator D that adds both the formalized consistency statement ¬Con(P) and the reflection principle □ₚφ → φ at each successor stage, with explicit recursive axiomatization at limit stages. Unlike Feferman's classical progressions which add only consistency statements, our strengthened operator enables earlier capture of Σ₁¹ truths, yielding the sharp Π₁¹ completeness result.
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Daniel Osipenkov
Smolensk State University
Smolensk State University
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Daniel Osipenkov (Thu,) studied this question.
synapsesocial.com/papers/697460e9bb9d90c67120ac5b — DOI: https://doi.org/10.5281/zenodo.18338606