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This article used to state that the Gödel–Gentzen negative translation of a formula is weaker than the original formula in intuitionistic logic, i.e. that intuitionistic logic proves φ → φN for any φ. [1] Is this an inaccurate statement? —Preceding unsigned comment added by Classicalecon ( talk • contribs) 12:40, 25 February 2009 (UTC)
I'm inclined to think it would make most sense to rework this article to something like Double-negation translation, that can deal with this, the Kolmogorov, and the Kuroda translations on an equal footing, and allow Glivenko's theorem to be merged here. The article would then be better placed to talk about the ingredients, i.e. the relevant logical equivalences, that form the basis of these translations. Thoughts? — Charles Stewart (talk) 08:48, 24 April 2009 (UTC)
Having noticed that the first section falsely claims that double-negating propositional formulae, I think it is plain that the topics above are best treated together, as indeed all is done by all the modern treatments I am aware of. I've put a mege notice on the article: my proposal is first to merge Glivenko's theorem into this article, and then to move the merged article to Double-negation translation. — Charles Stewart (talk) 09:21, 30 April 2009 (UTC)
I am not an expert in this subject at all, but on this page it says that Glivenko's theorem is:
Shouldn't this be:
where T* = { ¬¬θ | θ in T }? 77.169.36.17 ( talk) 22:10, 12 February 2015 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||
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This article used to state that the Gödel–Gentzen negative translation of a formula is weaker than the original formula in intuitionistic logic, i.e. that intuitionistic logic proves φ → φN for any φ. [1] Is this an inaccurate statement? —Preceding unsigned comment added by Classicalecon ( talk • contribs) 12:40, 25 February 2009 (UTC)
I'm inclined to think it would make most sense to rework this article to something like Double-negation translation, that can deal with this, the Kolmogorov, and the Kuroda translations on an equal footing, and allow Glivenko's theorem to be merged here. The article would then be better placed to talk about the ingredients, i.e. the relevant logical equivalences, that form the basis of these translations. Thoughts? — Charles Stewart (talk) 08:48, 24 April 2009 (UTC)
Having noticed that the first section falsely claims that double-negating propositional formulae, I think it is plain that the topics above are best treated together, as indeed all is done by all the modern treatments I am aware of. I've put a mege notice on the article: my proposal is first to merge Glivenko's theorem into this article, and then to move the merged article to Double-negation translation. — Charles Stewart (talk) 09:21, 30 April 2009 (UTC)
I am not an expert in this subject at all, but on this page it says that Glivenko's theorem is:
Shouldn't this be:
where T* = { ¬¬θ | θ in T }? 77.169.36.17 ( talk) 22:10, 12 February 2015 (UTC)