Serious High 1-B Question/Rant

[PrinceofPein]

So bassically you mean that a hierarchy like this, does not have a cofinality?

Pretty much

Are you saying that the verse does not satisfy a counting of real numbers or something like Aleph-1 + L? Nor something with combinations like V=L.
(To prove the existence of the many classes of elements etc exist)

Not sure what is your L and V in this mean

But if you mean that there is no proof of set progressions like counting real numbers then yes that’s what I mean
His example assumes that within each set there is another infinite set.
Which is different from counting of natural numbers which is a single set containing infinite members

 

[Makoto500]

Pretty much

Alright

Not sure what is your L and V in this mean

But if you mean that there is no proof of set progressions like counting real numbers then yes that’s what I mean
His example assumes that within each set there is another infinite set.
Which is different from counting of natural numbers which is a single set containing infinite members

Alright, well I was talking and asking about it not having anything like V=L or any assuming statement in the fictional verse to prove that the urrelements, elements and classes of zfc or real numbers exist in the verse.
(So it wouldn't get past an aleph 1 nor reach aleph-1 without assuming something like L is there or if we use the system of L.)

Though with the quoted thing above I guess this would be a yes.

 

[KingPin0422]

Moving on let's say you have a High 1-B Structure (The Original Structure) and inside of one of those dimensions (Let's call it Dimension A) is another High 1-B Structure. Now Dimension A which contains and transcends a High 1-B Structure in and of itself is Low 1-A.

This is your first mistake: simply containing a High 1-B structure does not make anything Low 1-A. Think of it like this: the set of naturals is encompassed by the set of integers, which is in turn a subset of the rationals, and yet all three of these sets have the same size. Similarly, the set of reals contains the set of irrationals as part of itself, but that doesn't make the reals a larger set than the irrationals. It's the same principle behind why multiple 2-A structures, unless further context is given, are not treated as larger than just one of them.

Going back to Dimension A as we are aware it has a High 1-B Structure (Structure A), so what if Structure A also had a High 1-B Structure within all of its dimensions?
Well according to what we just went over Structure A is 1-A+ as just one of its dimensions would be Low 1-A and the dimension above that would be 1-A, and the dimension above that would be another layer into 1-A all the way u to infinite layers which are 1-A+.

Ok so now Structure A is 1-A+, Dimension B transcends Structure A and encompasses it making it High 1-A and The Original Structure would be infinite layers into High 1-A.

This is not how High 1-A works at all. You don't reach the tier just by transcending something which is 1-A+ with no more context, especially if it's the same kind of transcendence that's used to reach 1-A+ in the first place. You also can't reach it by simply stacking hierarchies endlessly, which is what you are doing here. There are only two ways to be High 1-A:

1. Having an inaccessible size or number of higher layers/dimensions/what have you.
2. Exceeding the verse's basis for 1-A levels, such as by R-F transcendence in a verse where 1-A levels are defined by dimensions.

So according to all of that if I'm correct, if I put YET ANOTHER High 1-B Structure within the High 1-B Structures of Structure A, The Original Structure would be Tier 0. Ok so what about verses that have recursions?

A High 1-B Structure containing Infinite High 1-B Structures on each of its layers of which there are Infinite layers. And furthermore, each of those High 1-B Structures dimensions contains Infinite High 1-B Structures, which follow the same rules infinitely. A recursion system like this should by all means reach ridiculously high into Tier 0, like unbelievably so.

Even if everything you said up until this point were true, it wouldn't even come close to tier 0. Contrary to what seems to be popular belief, it doesn't go straight from inaccessibility to Mahloness- there are higher "degrees" of inaccessibility that each require their own axioms to be assumed. See here for a simple description.

(As a tangentially related side note, the definition of tier 0 at present is vague enough to where "objects which completely exceed the logical foundations of High 1-A" could simply be 1-inaccessible cardinals, as those technically do exceed the logic of High 1-A according to the provided source [which I can support with more sources if need be]. That it refers to Mahlo cardinals as a baseline is simply an informal consensus and not an official ruling, as far as I know.)

 

[ActuallySpaceMan42]

This is your first mistake: simply containing a High 1-B structure does not make anything Low 1-A. Think of it like this: the set of naturals is encompassed by the set of integers, which is in turn a subset of the rationals, and yet all three of these sets have the same size. Similarly, the set of reals contains the set of irrationals as part of itself, but that doesn't make the reals a larger set than the irrationals. It's the same principle behind why multiple 2-A structures, unless further context is given, are not treated as larger than just one of them.

Ya, I had to have those multiple ways of transcendence part explained to me by pain. But to make it clear, I was making this example under the guess the High 1-B Structure would exist and be transcended by the dimension of the other High 1-B Structure it is in.

 

[Gasper]

Ok, so this is going to be an extremely long question/rant since I really never understood how this works in our tiering system and kind of seems like a loophole. (For these examples below assume dimensions have transcendence.)

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So first of all there are two types of High 1-B Structures from what I am aware. The first is a structure that starts at zero dimensions and goes up to infinite dimensions and the second is a structure that has no start, it goes up into infinite dimensions as normal and goes down infinitely as well. For a normal High 1-B Structure, this is impossible as any dimension under the Infintieth Dimension would be Finite and therefore 1-B instead.

However, for a High 1-B Structure that is Infinite up and Down that means every dimension within it is technically High 1-B since Infinity/435345345 = Infinity.

That can potentially be low 1-A if this dimensions are infinitely superior to the last.

Alright so for any further examples when I say High 1-B I'm talking about the latter example and they all contain one another.

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Moving on let's say you have a High 1-B Structure (The Original Structure) and inside of one of those dimensions (Let's call it Dimension A) is another High 1-B Structure. Now Dimension A which contains and transcends a High 1-B Structure in and of itself is Low 1-A.

And the dimension above Dimension A (Dimension B) is 1-A as it contains and transcends Dimension A. So in total, this makes The Original Structure which was High 1-B, 1-A+, as this will continue up to infinity and 1-A+ is an infinite number of steps above 1-A.

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Ok, so this is where things start to fall apart in my brain.

Going back to Dimension A as we are aware it has a High 1-B Structure (Structure A), so what if Structure A also had a High 1-B Structure within all of its dimensions?
Well according to what we just went over Structure A is 1-A+ as just one of its dimensions would be Low 1-A and the dimension above that would be 1-A, and the dimension above that would be another layer into 1-A all the way u to infinite layers which are 1-A+.

Is that dimension A still spatial dimension or just a name fallacy? Because if it is that's just higher into high 1-B.

Ok so now Structure A is 1-A+, Dimension B transcends Structure A and encompasses it making it High 1-A and The Original Structure would be infinite layers into High 1-A.

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So according to all of that if I'm correct, if I put YET ANOTHER High 1-B Structure within the High 1-B Structures of Structure A, The Original Structure would be Tier 0. Ok so what about verses that have recursions?

A High 1-B Structure containing Infinite High 1-B Structures on each of its layers of which there are Infinite layers. And furthermore, each of those High 1-B Structures dimensions contains Infinite High 1-B Structures, which follow the same rules infinitely. A recursion system like this should by all means reach ridiculously high into Tier 0, like unbelievably so.

No, that is still high 1-B maybe low 1-A at best.

 

[ActuallySpaceMan42]

Already had this question answered but appreciate the effort.

 

[Gasper]

Oh sorry for wasting your time then

 

[Antvasima]

So should I close this thread now then?

 

[Gasper]

So should I close this thread now then?

Yeah i think you can.

 

[Antvasima]

Okay. I will do so.

Thank you to everybody who helped out here.