Shows that dilator-based and Spector-class generalizations of ordinal analysis are entangled via Σ¹₂-proof theory.
A classification of incompleteness statements
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Generalizations of Gödel's second incompleteness theorem are developed from definability and semantic perspectives, with Craig's trick analyzed in reverse mathematics and a new unified proof given for ω-model and β_n-model versions.
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Proof-theoretic dilator and intermediate pointclasses
Shows that dilator-based and Spector-class generalizations of ordinal analysis are entangled via Σ¹₂-proof theory.
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On some generalizations of G\"{o}del's second incompleteness theorem
Generalizations of Gödel's second incompleteness theorem are developed from definability and semantic perspectives, with Craig's trick analyzed in reverse mathematics and a new unified proof given for ω-model and β_n-model versions.