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3:56 AM

@EmilJeřábek, Noam: I have created the tag theories-of-arithmetic. (This is for the moment easily reversible as the number of questions is very small.) I included a short tag excerpt, please improve it if necessary. I'll request to moderators to rename all instances of peano-arithmetic as theories-of-arithmetic. Note that this can be done in (at least) 2 ways: making a synonym, or merging, see Martin Sleziak's explanation at editor's lounge. — YCor 19 hours ago

new-tag A new tag theories-of-arithmetic, see the above comment. Link to the tag-excerpt: mathoverflow.net/posts/374020/revisions

Q: What can be proven in Peano arithmetic but not Heyting arithmetic?

Hi. I'll confess from the start to not being a logician. In fact this question came up not from research but during a discussion with a friend about whether the classical proof that $\sqrt{2}$ is irrational can be made acceptable to an intuitionist. (It can be.) The question is: Are there any "n...

Martin Sleziak

4:38 AM

@EmilJeřábek and YCor: Just to be on the safe side, I will repeat that merging is a tool which has to be used carefully, since it cannot be reversed. (If a synonym is created without merging, then it can be cancelled and the posts will have the original tags - with the exception of questions which were edited while it existed. If the tags are merged, then tags are actually changed and cancelling the synonym does not restore the original state, to get back to it one would retag manually.) — Martin Sleziak 30 secs ago

Since YCor post and some comments explicitly mention that this advice comes from me, I wanted to stress this caveat. (I think it is an important thing to keep in mind if merging of two tags is being considered.)

Setting technicalities aside, I am not fully sold on synonym peano-arithmetic $\to$ theories-of-arithmetic. But certainly people like Noah Schweber or Emil Jeřábek have much more experience with the posts from this are than I do.

(Just for the record: at the time of edit, with amended request, the question has a balance of +5=8−3 votes and Noah Schweber's answer has a balance of +6=6−0 votes.) — YCor 14 hours ago

Yes, that is one thing to keep in mind that it might be unclear what upvotes/downvotes stand for. In this case, some of them might be for the original version and some of them for the edited version.

I can even imagine: +1 It is useful to have discussion on this. (In this case the vote does not express opinion in any direction. It was the case for my upvote, but I have retracted the upvote now after it was changed to a feature request.)

Less likely but also possible: +1 I disagree with this, but I appreciate that you have discussed on meta before doing any action on this. (On MO, changes done by mods without any discussion with the users are more frequent than, for example, on Mathematics.)

17 hours later…

YCor

9:45 PM

@MartinSleziak Of course it's unclear, at the very beginning there was even a negative balance (a general observation is that a positive/negative balance tends to attract positive/negative votes!). I just wanted to stress that the 3 negative votes (2 now) were done in the first version, where I suggested the name "arithmetic-logic" which led to criticism.

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