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Here is the place for voting. See Googology Wiki:Policy#Voting for general rules.

## User_blog:P進大好きbot/First_Order_Theory_beyond_Higher_Order_Set_Theory

Please, tell me what do you think about adding it to the mainspace. I think we can at least mention it in the largest valid googologism. I appreciate anyone to vote for it. — Best regards, Triakula 13:02, February 13, 2020 (UTC)

It is hard for me to review and judge the validity of the definition, but I vote yes for adding it to the mainspace as it appears to be original and strong. 🐟 Fish fish fish ... 🐠 13:19, February 13, 2020 (UTC)
Thank you for the vote. I couldn't say whether it is well-defined either, but since nobody in our community can disprove that it is the number which is defined by the strongest paradigm, possibly it should take this place. — Best regards, Triakula 14:00, February 13, 2020 (UTC)
In my opinion, even if the number isn't well-defined, it doesn't necessarily mean there should not be an article about it. There are articles about ill-defined numbers like BIG FOOT and Little Bigeddon. Rpakr (talk) 13:03, February 19, 2020 (UTC)
I agree, and it only reinforces the point that the article about Large Number Garden Number should be created. — Best regards, Triakula 15:18, February 19, 2020 (UTC)
I agree, we need an article about "the number from the large numbers garden" and about all this theory in the mainspace, since the number is a strong candidate for title of largest valid googologism (however, if no one can verify, whether the number is well-defined, then this fact should also be noted in the article). --Denis Maksudov (talk) 20:52, February 13, 2020 (UTC)
Thanks. There were times when Little Bigeddon and BIG FOOT have been considered the largest until P進大好きbot found mistakes in the definitions (though I think that only a small part of googologists understand the reasonings). Maybe somebody ever will find the mistakes in Large Number Garden Number (see comments in the blog post for the name), but until we don't have an explicit reasoning, I think it deserves to be considered the largest. — Best regards, Triakula 07:21, February 14, 2020 (UTC)

On a related note, should we also add the similar googologism to the second place of the largest valid googologism? — Best regards, Triakula 09:27, February 14, 2020 (UTC)

Since the work won the voting system and members of the panel are not against it, I'm going to add it to the mainspace. — Best regards, Triakula 08:35, February 25, 2020 (UTC)

Thank you!

p-adic 09:27, February 25, 2020 (UTC)

## User:Wythagoras/Dollar function

Because this function has been relatively important to googology over time, and is used on many pages, I propose addition to the mainspace. C7X (talk) 02:05, 31 December 2020 (UTC)

I agree that we should have an article about Dollar function --Denis Maksudov
Before judging the validity, I propose to solve known issues which have already pointed out here. Since the argument will be long, I hope that we will discuss it at the page.
p-adic 00:16, 2 March 2021 (UTC)
Oh, I'm sorry, I missed your message.--Denis Maksudov
p-adic 14:14, 5 March 2021 (UTC)

Now we have solved the issue in Talk:Dollar_function. To summarise, we obtained a direction: to clarify problems on the original source. In that case, I propose that it is good to note for readers' convenience that the source is the first but non-peer-reviewed source, and hence is not so reliable as other sources in the usual article.

p-adic 01:50, 6 March 2021 (UTC)

@The panel members

Since the period for voting finished, we should pass this to the panel members. If you think that the discussion has been fully given and we should allow this blog post as the valid first source of a new arctile due to the discussion, then please accept the proposal. Otherwise, please reject the proposal.

p-adic 08:31, 8 May 2021 (UTC)

I accept the proposal. 🐟 Fish fish fish ... 🐠 06:46, 25 May 2021 (UTC)
Thank you.
p-adic 09:50, 25 May 2021 (UTC)
I made the page. Dollar function. Actually I once created the page and Whytagoras stopped it for the rule at that time. 🐟 Fish fish fish ... 🐠 16:12, 5 July 2021 (UTC)
Thank you. I expanded the contents, following the proposal to include known problems.
p-adic 01:45, 6 July 2021 (UTC)

## Deedlit’ blogpost

In googological society Deedlit’ system of fundamental sequences was the first attempt to define fundamental sequences for functions, collapsing higher cardinalities (2013). It was important for googology and I propose to add this system in the mainspace’s article List of systems of fundamental sequences --Denis Maksudov

I agree with the significance, but the original source is not precisely written. For example, the FS for non-additive principal ordinal is ill-defined exactly by the same reason as the one explained in List of systems of fundamental sequences#Common misconception as a typical failure. Is there any solution? For example, could we ask Deedlit to fix all issues?
In my opinion, your works on Buchholz's function and Extended Buchholz's function is much more appropriate to be dealt with the first "succesful" trial to define FSs for OCFs. Your works are precisely written, are commonly used in googology (especially the most commonly used in Japanese googology), and have an external source. Isn't it sufficient to list your works instead of Deedlit's work?
p-adic 14:14, 5 March 2021 (UTC)
The rule which assign FS for non-additive principal ordinals seems correct:
If α=α_1+…+α_m then cof(α)=cof(α_m) and α[η]=α_1+…+α_m[η], where α_i are principal ordinals, α_1 ⩾… ⩾α_m
I see problems with normal form, since Deedlit doesn’t require α∈C(ν, α ,ϑ ν(α)). We can ask Deedlit to fix the problem, but he has been inactive for over a year.
Also can we write our own definition of normal form and point out that it was not taken from original post. From Deedlit’s post we will take only definition of ϑ-function and rules for assignation of FS.
> Isn't it sufficient to list your works instead of Deedlit's work?
Currently 6/9 sources are pages of my site. It is desirable that the article contains the works of as many different authors as possible. We also should write about Buchholz’s Uniform approach, but may be it is better to put it in separate article about norm functions.
--Denis Maksudov
> If α=α_1+…+α_m then cof(α)=cof(α_m) and α[η]=α_1+…+α_m[η], where α_i are principal ordinals, α_1 ⩾… ⩾α_m
Which page are you referring to? I was mentioning to this section, which does not require "α_i are principal ordinals, α_1 ⩾… ⩾α_m".
> Also can we write our own definition of normal form and point out that it was not taken from original post. From Deedlit’s post we will take only definition of ϑ-function and rules for assignation of FS.
It is good, if we calrify the issues in the original definition.
> Currently 6/9 sources are pages of my site. It is desirable that the article contains the works of as many different authors as possible.
I agree with it, as long as the sources are good. My point was the issues on the blog post. If we clearly clarify the problems in the source, then it is ok for me. (Maybe it is good to clarify that the original blog post is the first but non-peer-reviewed source and hence is not so reliable as other sources.)
> We also should write about Buchholz’s Uniform approach, but may be it is better to put it in separate article about norm functions.
Right. It is better. I am afraid that readers might believe as if hyp cos's work, which is of course significant in googogoly, is based only on his own work, while it is heavily based on Buchholz's great work.
p-adic 01:42, 6 March 2021 (UTC)
> Which page are you referring to? I was mentioning to this section, which does not require "α_i are principal ordinals, α_1 ⩾… ⩾α_m".
Yes, I mean the same section, but also taking into account the previous section. I quote Deedlit's text from the page:
...
Standard form
...
If α is not additively principal, then the standard form for α is α=α_1+α_2+…+α_n, where the α_i are principal ordinals with α_1≥α_2≥…≥α_n, and the α_i are expressed in standard form.
...
Fundamental sequences
...
We assume that the ordinal α is expressed in standard form.
...
If α=α_1+α_2+…+α_m, then cof (α) = cof (α_m) and α[η]=α_1+α_2+…+α_m[η]
...
end quote.
Thus, Deedlit didn't forget about α1≥α2≥…≥αn, but anyway we will rewrite the normal form, in particular because Deedlit didn’t require γ∈C(ν,γ,ϑ_ν(γ)) for case if α= ϑ_ν(γ).
--Denis Maksudov
> We assume that the ordinal α is expressed in standard form.
But this says nothing meaningful, as every ordinal in the context can be expressed in standard form. Isn't it precisely the same as the common mistake explained in the first paragraph of this section?
p-adic 15:10, 7 March 2021 (UTC)

And we can rewrite it for example in the same way as I did for other sections in the article:

Deedlit’s system of fundamental sequences

1. Definition of $$\vartheta$$-functions

...

2. Normal form for $$\vartheta$$-functions

We simultaneously define:

1. predicate $$_{DNF}$$;
2. set $$T_D$$ i.e. countable set of ordinals such that each element of the set can be denoted uniquely using only the symbols $$0,+,\Omega,\vartheta, \varphi$$ where $$\varphi$$ denotes binary Veblen function and $$\vartheta$$ denotes the hierarchy of collapsing functions defined in the previous subsection;
3. set $$P_D$$ (subset of $$T_D$$ which includes only additive principal numbers).

Definition of $$_{DNF}$$

1. $$\alpha=_{DNF}\alpha _{1}+\cdots +\alpha _{n}$$ iff $$\alpha =\alpha _{1}+\cdots +\alpha _{n}\wedge \alpha _{1}\geq \cdots \geq \alpha _{n}\wedge \alpha _{1},... ,\alpha _{n}\in P_D$$
2. $$\alpha=_{DNF}\varphi(\beta,\gamma)$$ iff $$\alpha=\varphi(\beta,\gamma)$$ and $$\beta,\gamma<\alpha$$
3. $$\alpha=_{DNF}\vartheta_\nu(\beta)$$ iff $$\alpha=\vartheta_\nu(\beta) \wedge \beta\in C(\nu, \beta, \vartheta_\nu(\beta))$$

Definition of sets $$T_D$$ and $$P_D$$

1. $$P_D \subset T_D$$
2. $$0 \in T_D$$
3. If $$\alpha=_{DNF}\alpha _{1}+\cdots +\alpha _{n}$$ and $$\alpha _{1},\cdots , \alpha _{n}\in P_D$$ then $$\alpha \in T_D$$
4. If $$\alpha=_{DNF}\vartheta_\nu(\beta)$$ and $$\nu,\beta\in T_D$$ then $$\alpha \in P_D$$
5. If $$\alpha=_{DNF}\varphi(\beta,\gamma)$$ and $$\beta,\gamma\in T_D$$ then $$\alpha \in P_D$$
6. If $$\alpha=\Omega_\beta$$ and $$\beta\in T_D$$ then $$\alpha \in P_D$$

3. Fundamental sequences

Fundamental sequences for non-zero ordinals $$\alpha\in T_D$$ were defined by Deedlit as follows:

List of Deedlit’s rules for assignation of FS

It looks good, as long as you clarify which parts are originally given by Deedlit. Also, I think that it is good to clarify the credit to you, because I think that you are the one who proposed the clear solutions for existing problems. In addition, I propose to clarify whether there is a written ordinal notation associated to it or not, as it is an important point in computable googology.
p-adic 12:35, 8 March 2021 (UTC)

@The panel members

Since the period for voting finished, we should pass this to the panel members. If you think that the discussion has been fully given and we should allow this blog post as the valid first source of a new arctile due to the discussion, then please accept the proposal. Otherwise, please reject the proposal.

p-adic 08:31, 8 May 2021 (UTC)

I accept the proposal. 🐟 Fish fish fish ... 🐠 06:47, 25 May 2021 (UTC)
Thank you.
p-adic 09:50, 25 May 2021 (UTC)

## R function

R function is a powerful recursive notation that may be on par with Strong Array Notation if both were formalized. I think it needs more attention than it is receiving right now. Please tell me your opinion of adding it to the mainspace. BTW, I am currently working on formalizing it, so even if it is originally unformalized, I may be able to completely formalize it in the future. Zongshu Wu 12:19, 8 March 2021 (UTC)

I agree as long as the article writes an alternative definition, because referring to an unformalised explanation is not good. Since you yourself are working on it, you should be evaluated as the one who is attempting to formalise it. For this purpose, it is good to ask others to check your alternative definition, because it is the key point of this voting in my opinion. I am sorry that I myself currently have few time. I hope some others will check your work carefully. I strongly recommend you to ask others to check your alternative formalisation before writing the article, because currently so many articles based on personal websites are poorly written. (You might remember that a blocked user wrote articles on the user's own ill-defined notations and repeated destructions so many times.) What do you think about?
p-adic 12:35, 8 March 2021 (UTC)

The definition is the section 1.3.

Zongshu Wu 13:47, 8 March 2021 (UTC)

@The panel members

Since the period for voting finished, we should pass this to the panel members. If you think that the discussion has been fully given and we should allow this blog post as the valid first source of a new arctile due to the discussion, then please accept the proposal. Otherwise, please reject the proposal.

p-adic 08:31, 8 May 2021 (UTC)

This is voting proposed here. Please tell us whethere you agree or disagree with the following topics:

1. Choosing User:ARsygo to be a new admin.
2. Relieving User:Cloudy176 from an admin.

Please check Googology Wiki:Policy#Voting. A single user cannot use two or more accounts in a voting. Only non-blocked users that were registered for at least 100 days (10 of them they were active) and 100 edits may vote to avoid abusing the voting system. Voting holds for 10 days. Please do not forget to add signature by writing four tildas.

Even if you agree (resp. disagree) with one of the topics, you can agree (resp disagree) with another one. Also, the voting right in this community is just a right, but not a duty. Therefore we do not force you to vote. (You can silently abstain from this voting, and you can express your decisions only for one or two of the topics.)

My decisions are:

1. I agree.
2. I agree.
3. I agree.

p-adic 00:09, 15 May 2021 (UTC)

Thought I am qualified to have a right for voting, I am going to vote:
1. I agree.
2. I agree.
3. I agree.
Kanrokoti (talk) 17:26, 15 May 2021 (UTC)
1. I agree.
2. I disagree.
3. I agree.
🐟 Fish fish fish ... 🐠 17:29, 15 May 2021 (UTC)
1. I agree.
2. I disagree.
3. I abstain.
C7X (talk) 18:45, 15 May 2021 (UTC)
1. I support it.
2. I strongly support it. Because Cloudy said, "I believe that copyright shouldn't exist", and tried to realize this belief through action.
3. I support it.
--Hexirp (talk) 04:05, 16 May 2021 (UTC)

Now ten days have been passed. I count valid votes:

1. Agreement : Disagreement = 5 : 0
2. Agreement : Disagreement = 3 : 2
3. Agreement : Disagreement = 4 : 0

I recall that choosing a new admin requires that the number of users agreeing to choose the candidates as a new admin is greater than or equal to twice the number of users disagreeing. This is the case (5 ≧ 2 × 0 = 0). Relieving an admin requires that the number of users agreeing to relieve the admin is greater than or equal to the number of users disagreeing. This is also the case (3 ≧ 2 and 3 ≧ 1). So, the result is that ARsygo is a new admin, and Cloudy176 and Username5243 are normal users now.

I would like to send words of praise to our new admin ARsygo, thank Cloudy176 and Username5243 for their past contributions to this wiki, and members to share their opinions! In order to proceed the execution, I would like members of the panel to check the result.

According to the rule, if there is no user with permission (that hasn't expired as a result of the voting) to execute these decisions, then we will ask FANDOM to execute these decisions. Since all valid bureaucrats are inactive in this community, I think that this is the case. Is there any opinion about it?

p-adic 04:39, 25 May 2021 (UTC)

I confirmed that the result is valid. I also suggest that there should be at least one bureaucrat, and therefore we ask FANDOM to set the active admin, C7X, to be a bureaucrat. 🐟 Fish fish fish ... 🐠 06:51, 25 May 2021 (UTC)
@fish
Thank you. I note that we have bureaucrats but they are inactive. (It is good to tell FANDOM the precise situtation.) I agree that there should be at least one active bureaucrat, because the lack of active bureaucrat is one of the reasons why we need this voting to choose a new admin.
@C7X
Do you agree to be a bureaucrat? (If you feel that one active bureaucrat is insufficient, it is good to make both of you and ARsygo bureaucrats. But I do not know whether one active bureaucrat is sufficient or not.)
p-adic 09:50, 25 May 2021 (UTC)
May 3. Agreement : Disagreement = 3 : 1 be 3. Agreement : Disagreement = 4 : 0? -- Hexirp (talk) 11:32, 25 May 2021 (UTC)
Oops, exactly. I corrected it.
p-adic 11:53, 25 May 2021 (UTC)
From the activity requirement, I can accept. But I don't know the tools that bureaucrats have, or what a bureaucrat is (other than that it's a high-ranking privilege) C7X (talk) 16:15, 25 May 2021 (UTC)
Bureaucrats can make a user an admin. (Help page)
p-adic 23:02, 25 May 2021 (UTC)
I think you may start a new voting. -- Hexirp (talk) 02:08, 27 May 2021 (UTC)
Sure, we can start a new voting after a month later. But we can also choose a usual way of decision, i.e. discussion. The reason why we need voting this time was because Username and Cloudy were not willing to listen to members' request (and Username were pretty eager to involve FANDOM to officially relieve himself rather than having fair discussion). On the other hand, we can basically discuss anything in this community as long as all active members can respect each other. So, it is good to spend days to discuss having a new bureaucrat. If we will not have a single decision, then it is good to have a new voting.
p-adic 03:24, 27 May 2021 (UTC)
I suggested to promote C7X to bureucrat in response to p-adic's "According to the rule, if there is no user with permission (that hasn't expired as a result of the voting) to execute these decisions, then we will ask FANDOM to execute these decisions. Since all valid bureaucrats are inactive in this community, I think that this is the case. Is there any opinion about it?" Normally the admin are set by buraucrat and FANDOM set buraucrat when the community has no buraucrat by adoption request. In this situation, the only buraucrat who has edited in a year is Cloudy176, and Cloudy 176's last edit was 30 April 2021 (no more than 60 days), so we could ask Cloudy176 to execute the decision, but Cloudy176 was relieved by the voting. This is a special case and I am not sure what we can do; maybe p-adic could ask FANDOM what we can do. 🐟 Fish fish fish ... 🐠 06:32, 27 May 2021 (UTC)
I agree with the promotion. One point is whether we should only promote C7X or both of C7X and ARsygo. If C7X feels OK to be a unique active bureaucrat, then it is ok. If C7X wants to share tasks (which appear perhaps at most once or twice in a year, I guess) with ARsygo, then it is good to reflect the opinion. Although I think that it is sufficient to have a single active bureaucrat, it is good to know what C7X wants to do.
Of course, I can ask FANDOM after the decision. (Or anybody else, especially members of the panel or active admins, are also ok.)
p-adic 08:49, 27 May 2021 (UTC)
We need to ask FANDOM to promote C7X for buraucrat. After that, C7X can promote anyone to buraucrat or admin. That is not FANDOM's work. 🐟 Fish fish fish ... 🐠 09:36, 27 May 2021 (UTC)
It makes sense. So, could I know whether C7X agrees with the direction or not?
p-adic 12:17, 27 May 2021 (UTC)
If promoting me to bureaucrat is the best course of action for active administration, I can accept. I don't know enough about the user ARsygo (other than activity) in order to say either way for their promotion C7X (talk) 16:22, 27 May 2021 (UTC)
I think that it is ok to consider and discuss after promoting you, as fish suggested. Then I will ask FANDOM to do so. (It perhaps cost a day, because I am busy today, too.)
p-adic 23:03, 27 May 2021 (UTC)
I noticed there are more inactive bureaucrats in this wiki, Ace45954 (inactive since 2013), Vel! (the creator / founder of this wiki, formerly known as Followed by 100 zeroes, inactive since 2018). What shall we do with them? Relieve it as well? ARsygo (talk) 02:37, 30 May 2021 (UTC)
As they are doing nothing, there is no reason to relieve. 🐟 Fish fish fish ... 🐠 07:17, 30 May 2021 (UTC)
If someone wants to relieve them in order to avoid future troubles, then he or she might propose to hold a voting. (FANDOM has an official rule to relieve too inactive admins, and hence they might be relived by FANDOM even if we do not vote.)
By the way, I asked FANDOM to execute the decision a few days ago. Perhaps the execution will cost days or a week.
p-adic 08:24, 30 May 2021 (UTC)
"FANDOM has an official rule to relieve too inactive admins" where is it written? 🐟 Fish fish fish ... 🐠 08:38, 30 May 2021 (UTC)
It is written in a Japanese help page "なお、既存のアドミン・ビューロクラット権限については、該当する方が1年以上活動されていない場合、喪失手続きをとらせていただく場合があります。", but I noticed that it is perhaps a wrong interpretation of "Existing admins may be removed only if they have been inactive for more than one year." in the corresponding English help page.
p-adic 09:53, 30 May 2021 (UTC)
I see. So as the request this time is a kind of adoption, they may remove inactive admins or buraucrats. This is not a rule that community should obey, but rather FANDOM's decision. 🐟 Fish fish fish ... 🐠 10:28, 30 May 2021 (UTC)
Request accepted. 🐟 Fish fish fish ... 🐠 16:11, 31 May 2021 (UTC)
Great.
p-adic 22:34, 31 May 2021 (UTC)

## User_blog:Kanrokoti/Subspecies_Primitive_psi_Function

I propose to put this notation into the mainspace. The reasons are following:

1. This is an additive notation which makes it easy to understand, because this notation is an extension of User_blog:P進大好きbot/Ordinal_Notation_Associated_to_Extended_Buchholz's_OCF.
2. I think this notation seems to be well-defined.
3. I think this is a few notation which is expected to reach $$\textrm{BM4}(0,0,0)(1,1,1)(2,2,1)$$ and actually given the definition.
4. I think this is a few notation which attempts to merge a nest notation and a sequence system, and I think this idea is very unique. (or maybe I just don't know the well-defined notations using the similar idea.)
5. I think the definition of this notation is relatively compact considering the reason 3 and 4.

I also think this notation is not appropriate for the mainspace. The reason is following:

1. This notation is not peer-reviewed well and not analyzed well. Therefore, this notation may contains serious problems like being ill-defined or doesn't reach the expectation. This significantly loses the purpose to put this into the mainspace I mentioned above.

Since I am the creator of the notation, it may contains some biases. So please tell me your thoughts and votes.

Kanrokoti (talk) 19:02, 6 July 2021 (UTC)

Good. Since it is a new notation and many of members in this community does not know the definition, I propose to set one month for members in this community to understand the behaviour and judge the notability in a fair point of view, before the voting. (For example, I do not know the behaviour.) Also, we appreciate if you make rough evidences of the reason 2 (such as a table) accessible, because it helps members to grasp the behaviour.
p-adic 23:28, 6 July 2021 (UTC)
Thank you. Let's set one month before voting. Since there is a googological event in this month in Japanese community, it is also good to submit this notation and wait for the analysis. BTW, I made the cheatsheet and put link in the blogpost, but its content is not well-informed. In case that this notation won't be analyzed in the event (I mean "殿堂入り" with no analysis), I think I should add some contents in the cheatsheet. I'm too lazy to do that tho.
Kanrokoti (talk) 07:02, 7 July 2021 (UTC)