AN INCOMPLETENESS THEOREM VIA ORDINAL ANALYSIS
- 12 September 2022
- journal article
- research article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
Abstract
We present an analogue of Godel's second incompleteness theorem for systems of second-order arithmetic. Whereas Godel showed that sufficiently strong theories that are Pi(0)(1)-sound and sigma(0)(1)-definable do not prove their own Pi(0)(1)-soundness, we prove that sufficiently strong theories that are Pi(1)(1)-sound and sigma(1)(1)-definable do not prove their own Pi(1)(1)-soundness. Our proof does not involve the construction of a self-referential sentence but rather relies on ordinal analysis.Keywords
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