A classification of incompleteness statements
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DOI: 10.4153/s000843952510091x
Abstract: For which choices of $X,Y,Z\in\{\Sigma^1_1,\Pi^1_1\}$ 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 G\"odel's second incompleteness theorem that hold within… read more here.
Keywords: incompleteness statements; incompleteness; classification incompleteness;