Low 1-A and above, where do terminologies like Type 4 Multiverse (and many others) scale to and why?

[demonwarrior2266]

So I've seen about the concept of a Tegmark Type 4 Multiverse itself. I've heard the term tossed around a bit, some saying it is giga-super-beyond-fiction-beats-goku-boundless, others say it is low 1-a, others say it doesn't actually scale anywhere, etc. All sorts of different answers, but I am not sure what the correct one is.

I've seen on a handy and dandy wikipedia article that says "This level considers all universes to be equally real which can be described by different mathematical structures", and i do believe some crazy cardinal numbers are apart of this definition (at least from what I can see after thinking about it superficially).

So where does it scale and why so?

The whole reason I am making this post is because I want to get acquainted with more of the higher tier terminology I see thrown around when scaling characters low 1-a and above, like v=ultimate l, modal realism, the reflection principle, etc, so if anyone can explain any of these in addition to tegmark type 4, (AS WELL AS ANY OTHERS YOU WOULD THINK WOULD BE NICE TO KNOW), this would also be helpful (especially v=ultimate l, I see that one quite a bit).

Finally, I've seen people on this forum that seem to have a competent grasp on this sort of stuff. How do you guys learn it? Is it some set of videos or articles or what have you, or is it surrounding yourself in it constantly until you just pick stuff up about it?

 

[demonwarrior2266]

ALSO If it is in a specific tier, tell me how HIGH it goes into that tier. Like if it is boundless then say how high into boundless, and same goes for the other tiers.

 

[Guardian_Doge]

Honestly, I was going to type out a really well thought out, sourced explanation, but I'm lazy. So let's make it easier.

A Type IV is the set of all possible and consistent mathematical structures introduced by its categories or formal system. For example, a type IV multiverse with the idea of vector spaces and topological spaces, would be the culmination of those formal systems entirely, i.e a set of all vector spaces with algebra extending over the field of real numbers. So, whatever systems you have in there, it will extend that formal system to its limit in order to remain self consistent.

The Ultimate L conjecture simplifies the nature of Large cardinals, to the level of a constructible set, meaning all those cardinals can be derived from a formula and within the previous parameters, like the set of even numbers can be derived from all numbers divisible by 2.

Modal realism, is about possibility and necessity, different worlds may have different physical structure and logical structure, you can invoke more than a type IV because it doesn't need to be self consistent, the worlds are spatially and casually isolated (unless they aren't Lol!)

As for the reflection principle uhh, basically the Universe is absolutely infinite, and you can either infer a potential universe of sets i.e the infinities we derive are lower classes of the Absolutely infinite, and we can never construct a full universe, or an actual universe of sets which is just that all those infinites exist already.

Finally, I've seen people on this forum that seem to have a competent grasp on this sort of stuff. How do you guys learn it? Is it some set of videos or articles or what have you, or is it surrounding yourself in it constantly until you just pick stuff up about it?

It is eternal suffering, you either forget it, get trapped in it, revel in it, or all of the above. Start small, then get bigger.

 

[demonwarrior2266]

Honestly, I was going to type out a really well thought out, sourced explanation, but I'm lazy. So let's make it easier.

A Type IV is the set of all possible and consistent mathematical structures introduced by its categories or formal system. For example, a type IV multiverse with the idea of vector spaces and topological spaces, would be the culmination of those formal systems entirely, i.e a set of all vector spaces with algebra extending over the field of real numbers. So, whatever systems you have in there, it will extend that formal system to its limit in order to remain self consistent.

The Ultimate L conjecture simplifies the nature of Large cardinals, to the level of a constructible set, meaning all those cardinals can be derived from a formula and within the previous parameters, like the set of even numbers can be derived from all numbers divisible by 2.

Modal realism, is about possibility and necessity, different worlds may have different physical structure and logical structure, you can invoke more than a type IV because it doesn't need to be self consistent, the worlds are spatially and casually isolated (unless they aren't Lol!)

As for the reflection principle uhh, basically the Universe is absolutely infinite, and you can either infer a potential universe of sets i.e the infinities we derive are lower classes of the Absolutely infinite, and we can never construct a full universe, or an actual universe of sets which is just that all those infinites exist already.



It is eternal suffering, you either forget it, get trapped in it, revel in it, or all of the above. Start small, then get bigger.

thank you my good man, i honestly think they should have a sort of extended terminology page for stuff like this

 

[demonwarrior2266]

Honestly, I was going to type out a really well thought out, sourced explanation, but I'm lazy. So let's make it easier.

A Type IV is the set of all possible and consistent mathematical structures introduced by its categories or formal system. For example, a type IV multiverse with the idea of vector spaces and topological spaces, would be the culmination of those formal systems entirely, i.e a set of all vector spaces with algebra extending over the field of real numbers. So, whatever systems you have in there, it will extend that formal system to its limit in order to remain self consistent.

The Ultimate L conjecture simplifies the nature of Large cardinals, to the level of a constructible set, meaning all those cardinals can be derived from a formula and within the previous parameters, like the set of even numbers can be derived from all numbers divisible by 2.

Modal realism, is about possibility and necessity, different worlds may have different physical structure and logical structure, you can invoke more than a type IV because it doesn't need to be self consistent, the worlds are spatially and casually isolated (unless they aren't Lol!)

As for the reflection principle uhh, basically the Universe is absolutely infinite, and you can either infer a potential universe of sets i.e the infinities we derive are lower classes of the Absolutely infinite, and we can never construct a full universe, or an actual universe of sets which is just that all those infinites exist already.



It is eternal suffering, you either forget it, get trapped in it, revel in it, or all of the above. Start small, then get bigger.

So what tier would type 4 be exactly? and why so? i'd ASSUME 0 because if it consists of all mathematical structures then things like large cardinals would apply right? or am i missing something

 

[Railgun]

So what tier would type 4 be exactly? and why so? i'd ASSUME 0 because if it consists of all mathematical structures then things like large cardinals would apply right? or am i missing something

You can check this thread. It simply doesn't scale anywhere without context.

Never mind, you've already commented there.