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World of Darkness: Cosmology 1.5 TM/INC/LLC/CR

Honestly, neither have time nor motivation to read deeply into that lore.
From a glance at the OP is literally the entire reason for the upgrade that the words "set theory" were mentioned once or was there some more elaborate explanation that goes with it?
 
set theory in platonic realm which makes the concept Set theory is complete and inaccessible from the physical world. I think there is a tendency for h1a to be close to absolute infinity.
 
Less of a specific being than a class of them, the Toposes are some of the most baffling denizens of the Platonic Realm. They can be found in the Digital Borderlands where each has carved out a territory where they make the rules. These territories only ever grow over time, and seem to relate to how much they've been visited. It pushed, some will suggest that the majority of the Platonic Realm itself is simply the territory of a single Topos that has grown particularly dominant: Set Theory. Each of them represents an alternate system of logic capable of handling a complex system of mathematics, albeit one that differs from the standard one in either subtle or obvious ways. As such, though they look largely human, each of them will have something about them that is ... off. Extra limbs, strange coloration, or being entirely flat are all variations that have been reported. Each is unique, and all of them are rivals, though more similar ones will get along better and have appearances that reflect their similarities. Visitors find the Toposes are particularly good for helping them solve puzzles. As alternate logics, they are able to produce strange and unexpected solutions to problems, exploiting information that seems disconnected but placing some sort of logical chain between them. They can provide training in Enigmas (even allowing characters to reach the sixth dot of it) as well as the mathematical Abilities of Science and Academics. All they want in exchange is Sleeper attention. The smallest of them especially will give quite a bit to have the visitors return to Earth and write a research paper studying their structures and promoting them as interesting environments in which to do mathematics. Especially if they can do so in a way that makes them look better than Set Theory.
-
And it seems like Toposes can do it better than set theory.
 
DontTalkDT said:
Honestly, neither have time nor motivation to read deeply into that lore.
From a glance at the OP is literally the entire reason for the upgrade that the words "set theory" were mentioned once or was there some more elaborate explanation that goes with it?
Click to expand...
There's mentions of specific axioms used in Set theory, such as the Axiom of Choice, which is used as a tool to Mages:

"The Axiom of Choice is a strange and controversial thing in Mathematics. As an axiom, it can neither be proved true or false, it's a basic assumption of the system. The controversial question is whether it is a "reasonable" axiom to use. There's several reformulations, and they range from "that should definitely be true" to "that's ridiculous, there's no way that's true" and yet, if one is, all are. On top of that, it allows some bizarre constructions. And all from the fairly simple rule: if you have a bunch of collections, you can pick one thing from each. The trick that make it viable in normal mathematics is that you know that there is some way to do it, but you might not be able to write it down.


The mind of mage, though, can actually find the choice. This brings strange, abstract things to reality. Whether they are infinitely complex cuts, strangely structured thoughts, or geometries that violate the very concept of length and area." - Paradigm Explored Number and Shape - Page 11
Click to expand...

As I said before, Ultima already evaluated the entire book and came to the conclusion of the rating High 1-A.
 
Udlmaster said:
There's mentions of specific axioms used in Set theory, such as the Axiom of Choice, which is used as a tool to Mages:



As I said before, Ultima already evaluated the entire book and came to the conclusion of the rating High 1-A.
Click to expand...
This is a great proof for proving the axiom of choice in ZFC.
 
Well, this basically falls into the category of "what if a character transcends mathematics without any specific structures mentioned", which I don't think we entirely settled yet. We had a thread where we decided that it's not tier 0 already, but we had yet to pin any more specific rating on it.
I can say that transcending regular set theory is at best 1-A+ even now, though, as it doesn't contain large cardinals and should hence be at least one infinite hierarchy of a different nature away from High 1-A.
 
DontTalkDT said:
Well, this basically falls into the category of "what if a character transcends mathematics without any specific structures mentioned", which I don't think we entirely settled yet. We had a thread where we decided that it's not tier 0 already, but we had yet to pin any more specific rating on it.
I can say that transcending regular set theory is at best 1-A+ even now, though, as it doesn't contain large cardinals and should hence be at least one infinite hierarchy of a different nature away from High 1-A.
Click to expand...
But wod set theory isn't just regular set theory though. It exists in platonic realms.
 
DontTalkDT said:
Well, this basically falls into the category of "what if a character transcends mathematics without any specific structures mentioned", which I don't think we entirely settled yet. We had a thread where we decided that it's not tier 0 already, but we had yet to pin any more specific rating on it.
I can say that transcending regular set theory is at best 1-A+ even now, though, as it doesn't contain large cardinals and should hence be at least one infinite hierarchy of a different nature away from High 1-A.
Click to expand...
Well, given that the Axiom of Choice and other Axioms are tools which Mages can selectively use, doesn't that in and of itself speak to the existence of a Set theory without the Axiom applied, meaning Zermelo-Fraenkel Set theory is 1 of the many different Set theories in WoD beyond the standard Axiomatic form of Set theory.

For example, in WoD there's a higher branch of Mathematics called "Hypermath", which is essentially Mathematics on the level of Mages, as their understanding of the Universe and their insights are utterly beyond that of a simple human (This is in the same book btw);

Hypermathematics

Not simply the advanced mathematics for the Awakened, Hypermathematics is a technique that uses the increased toolset available to mages to do advanced mathematics in ways that are difficult or impossible for Sleepers. Awakened mathematicians are capable of conceptualizing things far outside Sleeper existence, giving them access to objects Sleepers would have no interest in as they model phenomena completely alien to them. One branch of hypermathematics focuses on the study of these objects, making it possible to develop science that study the Umbra and spirits, like Dimensional Science developed by Tychoides for the Void Engineers or any number of strange Etherite theories.

Another substantive branch focuses on constructions. Traditionally, there are several methods of proving the existence of an object that doesn't provide a construction for it. Hypermathematics contains strange axioms that make those constructions concrete: they can always find the choice function guaranteed by the axioms of choice, for example, or build an object out of a proof by contradiction. The applied hypermathiciation can then actually preform these constructions, or approximations of them, in the physical world, resulting in bizarre and impressive effects.
Click to expand...
 
Gasper said:
But wod set theory isn't just regular set theory though. It exists in platonic realms.
Click to expand...
Makes no difference for the tier of transcending it.
Dread said:
May I have a thread link for this?
Click to expand...
Yes.
Udlmaster said:
Well, given that the Axiom of Choice and other Axioms are tools which Mages can selectively use, doesn't that in and of itself speak to the existence of a Set theory without the Axiom applied, meaning Zermelo-Fraenkel Set theory is 1 of the many different Set theories in WoD beyond the standard Axiomatic form of Set theory.

For example, in WoD there's a higher branch of Mathematics called "Hypermath", which is essentially Mathematics on the level of Mages, as their understanding of the Universe and their insights are utterly beyond that of a simple human (This is in the same book btw);
Click to expand...
Even accepting all of that, I don't think that's enough to imply large cardinals in particular, though.
 
DontTalkDT said:
Well, this basically falls into the category of "what if a character transcends mathematics without any specific structures mentioned", which I don't think we entirely settled yet. We had a thread where we decided that it's not tier 0 already, but we had yet to pin any more specific rating on it.
I can say that transcending regular set theory is at best 1-A+ even now, though, as it doesn't contain large cardinals and should hence be at least one infinite hierarchy of a different nature away from High 1-A.
Click to expand...
Given the nature of the universe existing as a Type IV multiverse, all of those mathematical structures would be instantiated within reality.
Which, to my understanding, would be at minimum High 1-A, given the basic assumptions I can make off the existence of Set Theory + Axiom of Choice. This would allow me to derive an infinite succession of Alephs and form a "set" of said Alephs. Which should be High 1-A as it is unreachable by an infinite hierarchy of increasingly larger 1-A structures to a 1-A+ degree.
From this, the universe should still qualify for High 1-A, meaning no changes to what is presented by this thread.
 
DontTalkDT said:
Well, this basically falls into the category of "what if a character transcends mathematics without any specific structures mentioned", which I don't think we entirely settled yet. We had a thread where we decided that it's not tier 0 already, but we had yet to pin any more specific rating on it.
I can say that transcending regular set theory is at best 1-A+ even now, though, as it doesn't contain large cardinals and should hence be at least one infinite hierarchy of a different nature away from High 1-A.
Click to expand...
Even then, a lot of the cosmology would scale higher into the tiering system
 
[
DontTalkDT said:
Makes no difference for the tier of transcending it.

Yes.

Even accepting all of that, I don't think that's enough to imply large cardinals in particular, though.
Click to expand...
axioms of choice show the existence of ZFC
Lewis said:
The smallest of them especially will give quite a bit to have the visitors return to Earth and write a research paper studying their structures and promoting them as interesting environments in which to do mathematics. Especially if they can do so in a way that makes them look better than Set Theory.
Click to expand...
This gives them a much better structure and knowledge than set theory and axioms of choice.
 
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We may extend this to the Von Neumann–Bernays–Gödel set theory which has a class system and the axiom Vk, which is a stronger axioms of choice than ZFC and this is probably why Ultima rated h1a based on the book's content evaluation..
 
Last edited:
Don't be rude to DontTalk. He is easily one of our most intelligent, knowledgeable, loyal, and crucial staff members.

I edited away the mocking meme above.
 
Strange memes posted in response to well-behaved and helpful staff members are almost always posted to mock and disrespect others.
 
The meme was response to this:

What if I just ask the author;

"What other axioms were you referring to in the Set theory section of [Insert book here]"

Don't talk wasn't even been talked about in his comment.
 
Okay. I apologise for the misunderstanding then, but memes are still inappropriate in content revision threads.
 
deonment said:
Given the nature of the universe existing as a Type IV multiverse, all of those mathematical structures would be instantiated within reality.
Which, to my understanding, would be at minimum High 1-A, given the basic assumptions I can make off the existence of Set Theory + Axiom of Choice. This would allow me to derive an infinite succession of Alephs and form a "set" of said Alephs. Which should be High 1-A as it is unreachable by an infinite hierarchy of increasingly larger 1-A structures to a 1-A+ degree.
From this, the universe should still qualify for High 1-A, meaning no changes to what is presented by this thread.
Click to expand...
High 1-A is large cardinal territory, which is already beyond Set Theory in its entirety and all its infinite infinite infinite infinite.... hierarchies, including all regular alephs. The difference between Set Theory and Large Cardinal can't really be described (for logic reasons) but we assume it to be "large" (that's why they are called large cardinals kinda).

Timeless said:
Even then, a lot of the cosmology would scale higher into the tiering system
Click to expand...
I have in principle no problem with stacking further levels unto it. (albeit I, again, have not looked that far into the lore of this)
Just that when it comes to Set Theory as basis, it should be stacking upon something 1A+, instead of High 1-A, which would correspondingly lower the other stuff.

Udlmaster said:
What if I just ask the author;

"What other axioms were you referring to in the Set theory section of [Insert book here]"
Click to expand...
Not sure if we would consider the answer and I generally don't support bothering authors for upgrade reasons.

Lewis said:
axioms of choice show the existence of ZFC
Click to expand...
The axiom of choice shows the existence of the Zermelo–Fraenkel axioms with the axiom of choice added? What?

Aside from being confused over the statement, ZFC doesn't contain Large Cardinals either.

Lewis said:
We may extend this to the Von Neumann–Bernays–Gödel set theory which has a class system and the axiom Vk, which is a stronger axioms of choice than ZFC and this is probably why Ultima rated h1a based on the book's content evaluation..
Click to expand...
Why would we? Was that ever mentioned?
 
Udlmaster said:
What if I just ask the author;
Click to expand...
Unrelated to this, but asking the author a question like this would go against our WoG rule set.
DontTalkDT said:
High 1-A is large cardinal territory, which is already beyond Set Theory
Click to expand...
The issue I mostly see here, is that even under this assumption stuff like the Umbra or the Void would still classify for both High 1-A and 0 since they operate on levels similar to Inaccessible Cardinal sets and inaccessibility with lower spaces.
 
DontTalkDT said:
High 1-A is large cardinal territory, which is already beyond Set Theory in its entirety and all its infinite infinite infinite infinite.... hierarchies, including all regular alephs. The difference between Set Theory and Large Cardinal can't really be described (for logic reasons) but we assume it to be "large" (that's why they are called large cardinals kinda).
Click to expand...
We currently define High 1-A as either being beyond the framework of 1-A or any extension of a 1-A hierarchy.
I don't have to bother with the former way to reach High 1-A, as the latter is enough.
Do you agree that an infinite amount of alephs can be iterated and extended off of Aleph Null?
Do you agree that from Aleph 2 and on, each additional Aleph is 1-A and infinitely more than the one before?
Do you agree that the class of all alephs is unreachable to this infinite extension of Alephs, despite Aleph Omega (1-A+) and cardinals infinitely more than it being a part of it?
If you agree, as this hierarchy cannot reach the class of all Alephs, then something of its size must be equal to High 1-A, given it being unreachable to any additional extension to a 1-A hierarchy.
So WoD would retain the tiering proposed within the OP.
 
DontTalkDT said:
I have in principle no problem with stacking further levels unto it. (albeit I, again, have not looked that far into the lore of this)
Just that when it comes to Set Theory as basis, it should be stacking upon something 1A+, instead of High 1-A, which would correspondingly lower the other stuff.
Click to expand...
👍
 
NBG is a set theory and a conservative extension of ZFC with a system of classes that can contain all sets. You say that all sets of aleph omega equal1-a+ which class system can hold large cardinal and sets. At least it should get h1a because it can allow classes to be defined by formulas whose quantifiers range over classes. NBG is finitely axiomatizable, while ZFC and MK are not.💀
 
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