Does a Set Theoretic Multiverse count as 1-A?

[VictoriaGenesisBOA]

So, apart from the traditional Von Neumann universe, there is set-theoretic multiverse, which contains configurations of axioms and theories instead of belonging to one theory. A set-theoretic multiverse can contain a lot, even unbounded and transfinite amount of Von Neumann universes.

Since it is like that, the universes are independent in operations. Operations within the Von Neumann universes will not affect and cannot reach the set-theoretic multiverse's total structure as the axioms are literally different across it, which sounds pretty 1-A.

A set-theoretic multiverse can also contain different things, and there are theories like MK (Which can iterate over proper classes) and higher-order set theories (Can iterate over relations, meta-relations, etc. depending on the order, modifying over those logical structures instead of just modifying elements like Low 1-A do), you can just put different theories with different foundations and orders into a set-theoretic multiverse, even if they are not compatible (Like ZFC with CH and ZFC without CH in one set-theoretic multiverse).

So will a set-theoretic multiverse be 1-A given sufficient structures (like including class theories similar to MK) and sufficiently high order (perhaps transfinite orders)? It may also be possible to model Modal Realism using a set-theoretic multiverse by modeling worlds using universes and universe clusters (A set-theoretic multiverse can contain every orders, and may model every theories within itself), which is more High 1-A.

 

[MeiouHades]

If I recall correctly, we used to tier the Tegmark Multiverse at Low 1-A (not sure if we still have that), and that's just a multiverse that sort of contains all mathematical structures, classical logic (and otherwise) including structures that are not expressible as sets or structures that don't fit nearly into any set-theoretic universe such as some category-theoretic and group-theoretic universes or classes. That said, these are still quantitative increases. There is no qualitative difference between a Von Neumann universe and what you're describing, transfinite differences ARE quantitative by their very nature, so I don't believe it'll be any higher than Low 1-A. Also don't get confused by older mathematical terminology, most modern textbooks on Set theory now replace the terms transfinite ordinals or cardinals with just infinite, which is realistically what they really are.

 

[VictoriaGenesisBOA]

If I recall correctly, we used to tier the Tegmark Multiverse at Low 1-A (not sure if we still have that), and that's just a multiverse that sort of contains all mathematical structures, classical logic (and otherwise) including structures that are not expressible as sets or structures that don't fit nearly into any set-theoretic universe such as some category-theoretic and group-theoretic universes or classes. That said, these are still quantitative increases. There is no qualitative difference between a Von Neumann universe and what you're describing, transfinite differences ARE quantitative by their very nature, so I don't believe it'll be any higher than Low 1-A. Also don't get confused by older mathematical terminology, most modern textbooks on Set theory now replace the terms transfinite ordinals or cardinals with just infinite, which is realistically what they really are.

Based on the last thread I asked about the Type IV multiverse, the Type IV in this wiki isn't assumed as a ultimate container, which will be High 1-A. Instead, it's just assumed as a set theoretic universe.

A Question About Logics and Type IV Multiverse

So, a Type IV multiverse is generally regarded as Low 1-A, but after some discussions and thinking, I found out these: 1. Classical logic (Governed by three laws of thoughts), paraconsistent logic, fuzzy logic and every consistent logical structures, no matter any order, are indeed considered...

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[MeiouHades]

Based on the last thread I asked about the Type IV multiverse, the Type IV in this wiki isn't assumed as a ultimate container, which will be High 1-A. Instead, it's just assumed as a set theoretic universe.

A Question About Logics and Type IV Multiverse

So, a Type IV multiverse is generally regarded as Low 1-A, but after some discussions and thinking, I found out these: 1. Classical logic (Governed by three laws of thoughts), paraconsistent logic, fuzzy logic and every consistent logical structures, no matter any order, are indeed considered...

vsbattles.com

It's not just assumed to be a set-theoretic universe, it is assumed to be an all-encompassing mathematical multiverse, though functionally they're both the same here because we do not, by default, assume that destroying a Tegmark Multiverse is superior to destroying a Von Neumann universe. That's not High 1-A though. As you were told in the previous thread, while it's true that the Tegmark Multiverse contains all mathematical logic (and illogic as well, yes), the wiki doesn't assume that. This is why we usually need extremely blatant statements for Tiers like High 1-A or beyond. By default, it's still just an all-encompassing mathematical container. As far as the wiki is concerned, it also contains mathematical structures that aren't ZFC-constructible, but we don't care. It's still just Low 1-A here without further context.

 

[VictoriaGenesisBOA]

It's not just assumed to be a set-theoretic universe, it is assumed to be an all-encompassing mathematical multiverse, though functionally they're both the same here because we do not, by default, assume that destroying a Tegmark Multiverse is superior to destroying a Von Neumann universe. That's not High 1-A though. As you were told in the previous thread, while it's true that the Tegmark Multiverse contains all mathematical logic (and illogic as well, yes), the wiki doesn't assume that. This is why we usually need extremely blatant statements for Tiers like High 1-A or beyond. By default, it's still just an all-encompassing mathematical container. As far as the wiki is concerned, it also contains mathematical structures that aren't ZFC-constructible, but we don't care. It's still just Low 1-A here without further context.

First, I didn't mean ZFC, I mean every theories, includes class theories, type theories, graph theories and all those theories.

Second, I know that the wiki separated Logic Mathematics from the rest and put it at High 1-A, but isn't it weird that if the maximal set-theoretical multiverse is Low 1-A, then Modal Realism, which can be modeled using the multiverse, will be less than 1-A, but it should be High 1-A, contradicting itself?

 

[VictoriaGenesisBOA]

Outerversal Tiering Contradiction?

So, I know I asked things about Set-Theoretic Multiverse in the last thread, but here is a problem: First, the wiki separated logical study (Modal Realism, etc. ) with the rest of mathematics. Putting most of mathematics at Low 1-A while logics at High 1-A. Unfortunately, mathematics isn't...

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