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• W2787237760 abstract "The proofs of Kleene, Chaitin and Boolos for Gödel's First Incompleteness Theorem are studied from the perspectives of constructivity and the Rosser property. A proof of the incompleteness theorem has the Rosser property when the independence of the true but unprovable sentence can be shown by assuming only the (simple) consistency of the theory. It is known that Gödel's own proof for his incompleteness theorem does not have the Rosser property, and we show that neither do Kleene's or Boolos' proofs. However, we show that a variant of Chaitin's proof can have the Rosser property. The proofs of Gödel, Rosser and Kleene are constructive in the sense that they explicitly construct, by algorithmic ways, the independent sentence(s) from the theory. We show that the proofs of Chaitin and Boolos are not constructive, and they prove only the mere existence of the independent sentences." @default.
• W2787237760 created "2018-02-23" @default.
• W2787237760 creator A5028651659 @default.
• W2787237760 creator A5081140591 @default.
• W2787237760 date "2018-10-01" @default.
• W2787237760 modified "2023-09-23" @default.
• W2787237760 title "On constructivity and the Rosser property: a closer look at some Gödelean proofs" @default.
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• W2787237760 doi "https://doi.org/10.1016/j.apal.2018.04.009" @default.
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