User blog comment:Flitri/An ordinal Collapsing up to the Least weakly Mahlo Cardinal/@comment-35470197-20190409053305/@comment-35470197-20190411225901

> X = Sup{a, b, c, …} translates to « X is the supremum of the sequence (a, b, c, …) »

Maybe you are misunderstanding the convention sup_{β < μ} α[β] (which you denote by Sup{β < μ} α[β]). It is not (the supremum of β < μ) times α[β], but is the supremum of α[β] where the index β runs through all ordinals smaller than μ.

Well, in order to set advices to be a suitable level for you, could you tell me how much you know about set theory? I first thought that you know sufficiently many because you need much knowledge to define OCF with weakly Mahlo, and regard errors in your manuscript just as kind of typos.

However, your errors looks like ones by colledge students who are not so familiar with traditional conventions on set theory, which are necessary for understanding weakly Mahlo. If so, then I need to reduce the level of an explanation.

Also, I strongly recommend that you should not use terminology which you do not fully understand, because it yields so much errors. If you want to use it, then please look up the precise meaning of it before you actually use. If you could not find the precise meaning, arguments containing those words must be incorrect because there is no evidence that you are using correct terminology.

If you ask me the meaning, I can tell you if it is tradinal one. It is not so good for me to spend time for pointing out such terminological errors. Therefore please stop using such terminology before you understand the meaning. Searching invalit use of words in sentences costs much time, while just telling the meaning of words you asked does not.

Only after then, I can understand what is precisely written.

> o_1 and o_2

Read my explanation here. The second strategy to construct (OT,<) is the one related to your approach. Here, constant terms like 0 and ω is regarded as a constant function.

Also, you know the ordinal notation associated to Buchholz's OCF, right? Then Buchholz's construction by translating the function symbol D to the actual function ψ is very clear. Therefore it is good to remember the construction again.