29 авг. 2012 г. · Gödel-Rosser Theorem: If PA is consistent then ψ is indecidible, therefore PA is incomplete.

23 окт. 2017 г. · Here I shall present very simple computability-based proofs of Godel/Rosser's incompleteness theorem, which require only basic knowledge about programs.

1 мая 2020 г. · To contrast, he brings up Rosser's Theorem, which does show that a system can't be both complete and consistent. To quote: In Rosser's proof, we ...

3 мар. 2015 г. · Rosser's formula is a syntactical object; you are working in PA, ie first-order arithmetic, and thus you can simply add to the language the defined predicates ...

27 сент. 2016 г. · Tennenbaum's theorem may be regarded as the model-theoretic analogue of the Godel-Rosser incompleteness theorem.

6 мар. 2011 г. · 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.

4 апр. 2013 г. · Rosser's trick is not actually necessary. It may be surprising but there is actually a simple computability proof of a general version of the incompleteness ...

2 мар. 2019 г. · First Incompleteness Theorem (with shades of Tarski): Every sound and reasonably expressive system of arithmetic contains true, but unprovable sentences.

13 янв. 2015 г. · Gödel's second incompleteness theorem states that in a system which is free of contradictions, this absence of contradictions is neither provable nor refutable.

2 февр. 2021 г. · The famous Gödel incompleteness theorems which, at least as I originally understood it, purport to prove that mathematics itself cannot be axiomatized.