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NOTE: I did try again to prove the Löwenheim-Skolem theorem.

My new question is here.


What are the rules and guidelines for attempting to prove the same theorem again?


Some notes specific to my situation:

I've been trying to learn model theory off and on for a little while. The way that I've decided to do this is to pick foundational results and try to come up with proofs of them without consulting the textbooks I'm using, except for definitions.

The last time I tried to do this, my proof attempt was invalid, but I learned something useful from the commenter.

Attempted Proof of Löwenheim-Skolem theorem

I want to try again fairly soon, but want to do so in a way consistent with the rules, guidelines, and norms of the site/community, assuming of course that such a thing is possible. Editing a question with a completely new proof attempt might work and be preferable in my case, but it would not be a good option if the original question already had an answer.


What are the current rules as they stand now?


If there isn't an explicit rule for this, I propose the following rule for consideration

  1. You must wait 90 days before posting a new solution attempt.
  2. The approach taken by the new solution attempt must be substantially different from all previous attempts.
  3. You must include a link to all previous attempts in your new attempt.

Also, do these sorts of questions benefit the community? I think they have some value when the proof attempt is actually correct, because the asker will not use advanced techniques outside their background.

Some links to previous discussions that I can find:

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    $\begingroup$ I've wondered if there should be a "proof review" stackexchange analogous to the Code Review stackexchange. It would help people learn to write proofs. $\endgroup$ – littleO Jan 9 at 8:43
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The main danger with asking multiple questions on a single theorem is that you could easily write several posts where the effort required from answerers is duplicated from question to question - for instance, if answerers must read significant chunks of identical text or point out the same error over and over.

This doesn't rule out asking about multiple proofs of the same question (even over a reasonably short period), but you should take special caution if you do so.

  1. Write a good question! There's plenty of meta posts addressing proof verification questions in particular which probably contain some collected wisdom on how to do this. This is worth bringing up since I think the stronger each question is individually, the less likely there are to be problems between them - for instance, if questions are requiring a lot of duplicated effort, it's likely that the questions were too broad to begin with and would maybe benefit from being narrowed to particular lemmas or steps in a proof.

  2. Don't repeat yourself. If you're playing with small pieces of a larger proof, it is not justifiable to post two questions containing the same big proof with minor changes to a lemma between them and to ask, "Is this correct?". This is mostly a corollary of (1), since a question that is just a long proof with a general question about correctness is probably not the best question the author could have written (e.g. they could highlight where they are uncertain or focus on smaller pieces - potentially including or sketching the larger proof, but more for the purpose of context than as the strict content of the question).

  3. Don't make answerers repeat themselves. Make every effort to ensure that if you ask about two proofs, they don't contain the same flaw. Sometimes this might mean that you realize you didn't understand an answer to a previous question and should probably go back and comment there. Sometimes this might mean that you should, in a subsequent question, fix the proof and call out the error that was previously identified and why you think it's fixed - to ensure that, at least if the same flaw reappears, answerers can at least be more specific about it and more clearly understand your misunderstanding. (For this reason, you should almost certainly wait at least until you've received a good answer to any prior question about a theorem before posting another - though there's no requirement to wait longer than it takes you to get good answers, fully understand those answers, write a new proof, and write another high quality question)

  4. Linking prior attempts is sensible; links can provide a little extra protection against duplicated effort and maybe a slight amount of context - but don't rely solely on links to make a question good. Answerers should not need to click a link to write a good answer.

In your case, I think you'd be best off editing your existing question if you're just updating a small piece of the proof (treating the comments you got as a suggestion of "you should fix this in the question to avoid a trivial answer" rather than as an answer in itself). If you've written something totally separate, you should write a new question - and, if you're no longer interested in an answer to the previous one, it'd be fine to delete it since no one has written an answer.

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