A classification of incompleteness statements

2024/09/09 by Towsner, Henry, Walsh, James
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2409.05973

Abstract

For which choices of X,Y,Z∈\Σ¹₁,Π¹₁\ does no sufficiently strong X-sound and Y-definable extension theory prove its own Z-soundness? We give a complete answer, thereby delimiting the generalizations of Gödel's second incompleteness theorem that hold within second-order arithmetic.

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