I hope it is OK to ask this like this here. I thought about asking on MO, but then I was warned because once I had a question that was not appropriate.

I also was told once how my questions are not explained very well on SE. I hope I improved now.

I'd like to invite people from MO to have a look on my questions on SE, if they're interested/ experienced in logic, specifically proof theory, foundations, incompleteness, provability, meta-math...

They might be too difficult for SE, so maybe I should have posted them on MO. Maybe they're just bad, though, I'm not sure. Or even too easy?

I worked through a textbook of proof theory, the first chapter, I got along quite OK, but fail pretty seriously on most of the exercises. I could solve more or less accurately some of them with the help of others, but most questions are unsolved yet, some of them up to a month old.

Great if someone can give me some further explanations, hints etc...

Kind regards, Ettore



Question: When I would post my questions on MO, would it be OK to just write one single question in which I broadly describe what my difficulties are about and then leave a link to my questions? Or at least can I just open for each of my questions on SE one on MO and then just copy-paste the link, or is that even not allowed? Or do I have to copy-paste the whole textbody? It seems to me a bit overloaded to have both questions simultaneously on both sites, so I would just like to draw attention on my questions from experts, without being pushy, of course.

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    $\begingroup$ Question simulposted to meta MO, meta.mathoverflow.net/questions/4029/… $\endgroup$ – Gerry Myerson Dec 15 '18 at 17:29
  • $\begingroup$ Hello Gerry. Thanks for your comment! Yes, I know, why not? Is that a problem? Regards $\endgroup$ – Ettore Dec 15 '18 at 17:47
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    $\begingroup$ Did you read the comments below the answer, Ettore? Because if you did, you'd see that your questions, IF properly phrased, might work well on MO. So I would not link to your questions here, on MO. If I were you, I'd properly rephrase your questions anew, if you plan to post on MO. $\endgroup$ – amWhy Dec 15 '18 at 20:35
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    $\begingroup$ Ettore, in general, SE discourages the cross posting, simultaneously, of a question on two or more separate sites. So yes, it is a problem that you cross posted as you did. $\endgroup$ – amWhy Dec 15 '18 at 20:37
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    $\begingroup$ Just to help diminish confusion, SE refers, typically, to the Stack Exchange Network of sites, including mathematics.se, and mathoverflow.se, and over one hundred other sites. This site that you have posted to here is not known as SE. It is known as mathematics.se, one site among 140+ sites on the SE network. mathoverflow.se (MO) is one other site such site, among the 140+ sites on SE. $\endgroup$ – amWhy Dec 16 '18 at 0:12
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    $\begingroup$ I don't think that the difficulty of the questions (in the usual sense of the word) is an issue. Most of them are on relatively introductory issues in graduate-level proof theory - so they are technical, but there are several users here who are familiar with the topics. As I wrote below, I think the bigger issue is the time and effort that would be required to write a full answer for them. There are ways to ask very difficult questions so that they can still be answered with less effort. $\endgroup$ – Carl Mummert Dec 16 '18 at 3:53
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    $\begingroup$ One problem, Ettore, is that you didn't link your post on each site to the other one. Transparency is important here. You should make it easy for people to see what's going on. $\endgroup$ – Gerry Myerson Dec 16 '18 at 7:43
  • $\begingroup$ Thanks to everybody for your great comments, that helps! I will try to do better. I do read comments and try to improve myself. @Carl: Yes, I think that was also my intuition. And that's of course perfectly OK. I don't expect anyone to invest to much. I just wanted to be sure what's going on. $\endgroup$ – Ettore Dec 16 '18 at 10:00
  • $\begingroup$ @amWhy: Dear amWhy, if you'd like to add something to what Carl wrote in order to better my questions, you're very welcome. Regards.. $\endgroup$ – Ettore Dec 16 '18 at 11:15

I have answered or commented on some of the questions of the OP, which are very much in my area. I can propose a possible reason why "most questions are unsolved yet, some of them up to a month old". Of course, many people on this site are willing to try to answer technical questions, and at least in logic there are a number of experts active here and also on MathOverflow. So the issue is not a lack of expertise or activity.

Most of the questions I have seen from the OP are specific exercises from a relatively obscure graduate level textbook/monograph in mathematical logic. These questions are certainly on-topic on Math.SE, but for reasons I'll explain I am not surprised they receive few answers.

For a specific example, consider this question. To answer it, someone would need to have the required background knowledge, look at a copy of the book in question, think through what the author is saying, and then write an answer that tries to explain it. The post also has 6 numbered subquestions.

Answering that post would require far more effort than a question that simply asks about a mathematical concept and which an expert could answer without looking at any references. Answering one question like the one linked might require half an hour or more of dedicated work, assuming the answerer has access to the textbook, in order to write a coherent and detailed answer. So answering 10 or 20 questions of that sort is impractical for volunteers.

This site can be used for self-study, but as the OP has seen it quickly becomes impractical to use this site that way at the advanced graduate level. As a general principle, this site cannot replace a good in-person graduate program in which someone has classes that teach the background systematically, and has access to expert professors who are dedicated to helping their own students. This true for many technical graduate subjects, not only logic, but proof theory is sometimes considered a particularly difficult topic for self-study, because the literature is particularly obscure.

Questions will be more likely to be answered quickly if they refer to something where an expert can type an answer off the top of her head in a few minutes. So here is my advice is to maximize the chance a question is answered quickly:

  • Write questions about concepts rather than about specific textbook exercises.

  • Include all needed definitions (even quotes from books) in the post, so that there is no confusion about the definitions that are intended.

  • Write questions that do not require experts to look up any references, and particularly avoid questions that require specific obscure references.

  • Avoid listing numerous subquestions in a single post - these make it much more difficult to write a focused answer quickly

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  • $\begingroup$ Thanks again! I'll try to do better. I choose this textbook because it seemed the only one to do (reductive) proof theory and its philosophy on a throw, at once, which seems to me appropriate, and is more suited to my interest than a purely 'technical' book or a purely philosophical on reductive proof theory, if such a book even exists. (I would be interested in a introduction in the foundations of mathematics, but what I came across, few years ago, as far as I remember, was difficult to understand.) $\endgroup$ – Ettore Dec 16 '18 at 10:14
  • $\begingroup$ Of course I don't demand anybody to answer. I am just trying to find out how to use the site properly. Would you suggest another intro for self-study? So in general it would be alright to leave a link to a (potentially corrected/changed version of a) question of mine? $\endgroup$ – Ettore Dec 16 '18 at 11:14

Are my questions too difficult for SE?

No. But more importantly, it's not the perceived difficulty of a question that determines whether it's a good fit for MSE or MO. Any math question that's self-contained, isn't too broad, is well-written (and more generally is a well-asked question) is welcome. Sometimes people ask questions that end up not being answerable, and that's fine.

The content of your questions seems mostly to come from exercises from books. This content is certainly on topic here.

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    $\begingroup$ I disagree with the last paragraph. Some of those questions, properly phrased, could be naturally placed and would be well received on MO. $\endgroup$ – Andrés E. Caicedo Dec 15 '18 at 16:40
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    $\begingroup$ @AndrésE.Caicedo I'm glad you spoke up, then, so as to not give the OP the wrong idea. Perhaps I chose a poor subset of his questions to look at (or perhaps my unfamiliarity with logic is showing). Thank you - I'll edit my post. $\endgroup$ – davidlowryduda Dec 15 '18 at 16:43
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    $\begingroup$ The "properly phrased" bit in my comment is important. Several of the questions I looked at would need some rephrasing and refocusing before being appropriate to post there, but the topics are certainly things that come up on MO with some frequency. $\endgroup$ – Andrés E. Caicedo Dec 15 '18 at 16:49
  • $\begingroup$ @AndrésE.Caicedo Thanks a lot to both of you! I see...usually I just copied the exercise from the book. Sometimes I had troubles with notation or a proof, then I tried to explain this. I wonder what I should change. Maybe I should post the questions and then I would see what/how to improve by the comments etc... please also leave a note to the new question, I edited the post. $\endgroup$ – Ettore Dec 15 '18 at 18:06
  • $\begingroup$ @davidlowryduda see comment above $\endgroup$ – Ettore Dec 15 '18 at 18:06
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    $\begingroup$ @Ettore: When you make a comment on someone's answer, they always get notified. Even if you don't ping them. (Case in point, davidlowryduda will get notified on this comment, despite not being pinged.) $\endgroup$ – Asaf Karagila Dec 16 '18 at 8:31

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