User blog comment:PsiCubed2/My own version of BMS/@comment-35470197-20181120231600/@comment-35470197-20181121220508

> The notation proposed here is basically BM1 with a tiny modification. In fact, it resembles the original (faulty) PSS far more closely than all the wacko new versions (which are, apparently, so complicated that no-one knows how to write down an explicit rule set).

That is actually good. BUut if your proof is applicable to the halting problem of no other existing BMS, then it should be clearly declared instead of just stating that you have a work on the termination of your version of PSS.

> And I gotta tell you, that you're just being rude now.

I am sorry about it.

> How would you like it if someone had written such a sarcastic remark aimed at your 72-page proof? "Hey, it's not PSS, because you created a different set of rules".

I can tell them why it is remarkable, because it is applicable to several versions of BMS, as I stated to you months ago.

> Would you've liked that? Probably not. So why are you doing that to others?

It is because you have already done a similar thing... How could you say "I guarantee you that the proof for the notation presented here (assuming it works properly) will be far shorter than 72 pages"? It is obvious, because we are dealting with completely different problems. Even if you verified another open problem such as an upper bound of Laver's function, it is not appropriate to state that you can write a proof far shorter than the length of my proof.

Actually, the person who wrote the "hardly helpful" comment "you will need as many months as I spent because the difference between the expansion rule of PS and the fundamental sequence of Buchholz's ordinal notation system yields tiresome ramifications of arguments", but it was don before we share the information of the difference of the problems which we solved.

But well, I should be more polite, as you say. I am sorry for my behaviour.

> Is the version of PSS that you've defined in your proof closer to BMS than the version I've create above?

I only formulated PSS, because I have no idea to create one which works for trio sequences.

> Given that my version is BM1 with a very small modification, I really don't see how this can be possible. So if you want to shoot down my version as "not really PSS", you'll have to shoot down your own version as well.

No, because I was talking about the applicability to other versions of BMS.

> BTW I already have a pretty good intuitive idea how to create a 1-to-1 correspondence between the rule-set given in my blog post and the Buchholz system. But since I haven't yet written a formal line-by-line proof, I'm not 100% sure that there's no flaw in the reasoning. I do know, however, that I won't need anywhere near 72 pages to write down the entire thing, because it's a pretty straight-forward argument.

Writing a correspondence needed only 1 page. Verifying the comparison of the expansion rule needed almost all of those pages. But if you could write the "entire" thing so shortly with "pretty straight-forward argument", then you are just smarter than me. Good. Please go ahead. I have completely no idea how to write a complete proof within 10 page because PSS and Buchholz's ordinal notation system have completely distinct expansion rules.

Well, could you tell me then the precise difference of the expansion rules? If you think that you can prove the comparison, then you must know it, although I need many pages to determine it.