I request readers to revisit my old question. The problem is not solved yet even if another 4 months passed.
Let me briefly mention the situation again. I am a PhD student in mathematics and two years ago I discussed with an established mathematician about collaboration on a research project and he agreed. Then I worked on myself without his help and wrote the paper and sent to him. He raised some errors in two of the results and then I myself corrected those errors. After correcting the paper I sent back to him for final checking in language part, paper style etc. Since then it has been 10 months but he is not cooperating rightly. When I asked the old question 4 months ago, he didn't respond my email for 2 months. Two months ago he replied and again promised that he will finish it within next 2 weeks and he is very with the work but already more than 1 month passed, I got no reply on emailing him. This drama has been continuing since last 10 months, sometimes he replies and promise but ultimately he does nothing. As mentioned in my old question that we have no contact in person possible as we live in different countries but we have met several times in online meeting. I have given him all possible options as well. For example, I proposed him that since he is very busy then we might join online and he can advice me which parts of the paper needs further language change or which part require proper orientation. By the way, I told him that I am very confident that no mathematical error is there so that we don't need much time to discuss. But he is not even replying on this even if he did the promise 1 month ago.
I am very exhausted now, very worse experience, I am a PhD student and soon want to apply for Post doctoral position and I want to add the paper at least the preprint in my CV. I mentioned him about it but he is not caring it. Besides that the work is already 2 years old, others might work on similar problems, so it better we submit the paper atleast in arxiv. On the other side, he is not even leaving the deal, when he replies he says he will do it next week but in vain. He is a established mathematician, so he might have urgency in paper publishing but I need some good publication. In my opinion, he doesn't deserve a authorship in the paper as he didn't do anything besides picking some errors. But still I offered him authorship thinking of several aspects (e g., I will have new collaboration, may be a good journal will care the paper in proper way since he is a established mathematician etc).
But I now feel I should not wait anymore time. So I would like to inform him that if he doesn't finish his part in a month or so I will suppose he is not interested in this paper, in that case I will submit the paper without his name, instead I can acknowledge him only.
How to tell him the above words in nice way so that he can understand me or doesn't offend him ?