Question for Aleph omega

[IbnuValex]

I want to question what Aleph Omega is, to be honest, I'm a little confused.

I also want to ask what are the requirements to enter tier 1A+?

What is an Inaccessible Cardinal? How do you apply it to fiction?

 

[GarrixianXD]

This is the FC/OC general discussion but I'll answer for you anyway.

Yes, aleph-ω is High 1-A 1-A+ as omega is correlated with infinities.

An inaccessible cardinal is basically an uncountable cardinal (an uncountable infinite set of numbers/elements).

 

[Larssx]

This is the FC/OC general discussion but I'll answer for you anyway.

Yes, aleph-ω is High 1-A as omega is correlated with infinities.

No, cardinals don't give tier on their own, but I'm going to assume we're applying them to any object.
If there are as many objects or universes as aleph-ω, it will be 1-A+.
Even aleph-ω1 is equal to 1-A+ anyway.
H1-A is transcend the whole logical frame of 1-A.

An inaccessible cardinal is basically an uncountable cardinal (an uncountable infinite set of numbers/elements).

It's not that simple, really.
An uncountable infinite set simply begins with Aleph 1.
Anyway for inaccessible cardinal
It has to satisfy 3 conditions;
It must be uncountable: κ > Aleph-0;
It must be regular: which means it's not equal to the union of less than κ many sets with less size.
It must be a strong limit cardinal: whenever we have λ < κ then 2^λ < κ.

 

[GarrixianXD]

Aleph-ω is 1-A+ I mean, my bad.

 

[GarrixianXD]

It's not that simple, really.
An uncountable infinite set simply begins with Aleph 1.
Anyway for inaccessible cardinal
It has to satisfy 3 conditions;
It must be uncountable: κ > Aleph-0;
It must be regular: which means it's not equal to the union of less than κ many sets with less size.
It must be a strong limit cardinal: whenever we have λ < κ then 2^λ < κ.

Same thing. Aleph-0 is the peak of a countable cardinal.

 

[Larssx]

Same thing. Aleph-0 is the peak of a countable cardinal.

I mean it is not correct to just say "uncountable infinite cardinal" for the Inaccessible cardinal.

Aleph-ω is 1-A+ I mean, my bad.

No problem.

 

[GarrixianXD]

An inaccessible cardinal is uncountable, every infinite cardinal applies to it including Aleph-0 contradictorily… For the case with our tiering system I’m sure any tiering above High 1-B is required to be uncountably infinite

 

[Larssx]

An inaccessible cardinal is uncountable, every infinite cardinal applies to it including Aleph-0 contradictorily… For the case with our tiering system I’m sure any tiering above High 1-B is required to be uncountably infinite

It is not wrong that it is uncountable, it is just an inadequate explanation.
I am not implying that you are wrong in what you say.