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Given a theory (say $T$) which satisfies the hypotheses of the Godel- Rosser theorem. How to show whether a Rosser sentence $R$ for $T$ is true for the standard interpretation ($\Bbb N$) or not?.

(I know it is true but how we can prove this claim!)

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    Isn't Rosser's sentence: "If this sentence is provable then its negation is provable with a proof of smaller Gödel number than this one's"? If so, if arithmetic is consistent then if $R$ was provable then its negation would be provable. This is impossible. Thus it's not provable therefore it's true.2011-03-06
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    Rosser's sentence: "If this sentence is provable then its negation is provable with a proof of smaller Gödel number than this one's"! yes it is.2011-03-06

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