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I'm learning tier

H1a katmaIs there an endless hierarchy to move from H1a to layer 0, as in 1a?
First, no, it is not enough to reach H1-A from 1-A by adding a infinite hierarchy on top of 1-A or to transcend that hierarchy etc. The relationship between the inaccessible cardinals and alephs is not that simple.

Secondly, since the difference between 0 and H1-A is in the same logic as the difference between 1-A and H1-A, adding an infinite hierarchy on top of H1-A or transcending this hierarchy is not enough to become tier 0.
 
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H1a katmaIs there an endless hierarchy to move from H1a to layer 0, as in 1a?
It's not just "endless" or "infinite" but there are an inaccessible amount of layers between H1-A and 0 as there are between 1-A and H1-A.
First, let's start with this explanation: Transcending H1-A qualitatively or seeing it as a fiction will give you 1 layer in H1-A, just as you gain 1 layer in 1-A, and you can make it even larger. For example, imagine a hierarchy, there are infinite layers in this hierarchy and At the bottom of the hierarchy there is a H1-A place, in this hierarchy the places are stacked on top of each other and each place transcending the other qualitatively or sees it as a fiction. This hierarchy will take you to the infinite layer in H1-A. To go beyond this and transcending this hierarchy is not enough for tier 0, it just puts you on a higher layer in H1-A, all you have to do is be inaccessible to this hierarchy for tier 0.

Another explanation of layers would be:
Well, on the wiki you can still use the power sets to transcend layers at H1-A or 0, Which means you can say that
0-innaccessible is baseline H1-A, P(0-innaccessible) is 1 layer in H1-A and P(P(0-innaccessible)) is 2 layers in H1-A, If you repeat this power set operation infinite times, you can go to the infinite layer in H1-A, but as in 1-A and H1-A, it is not enough just transcend infinite layer to reach tier 0.
For tier 0 you have to transcend this whole 0-innaccessible hierarchy in an inaccessible way. To explain this better, if you define λ as a cardinal in any 0-innaccessible hierarchy, whenever we have λ<κ there is 2^λ < κ, so here no matter how big you make λ, it will still be smaller than κ.
 
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It's not just "endless" or "infinite" but there are an inaccessible amount of layers between H1-A and 0 as there are between 1-A and H1-A.
First, let's start with this explanation: Transcending H1-A qualitatively or seeing it as a fiction will give you 1 layer in H1-A, just as you gain 1 layer in 1-A, and you can make it even larger. For example, imagine a hierarchy, there are infinite layers in this hierarchy and At the bottom of the hierarchy there is a H1-A place, in this hierarchy the places are stacked on top of each other and each place transcending the other qualitatively or sees it as a fiction. This hierarchy will take you to the infinite layer in H1-A. To go beyond this and transcending this hierarchy is not enough for tier 0, it just puts you on a higher layer in H1-A, all you have to do is be inaccessible to this hierarchy for tier 0.

Another explanation of layers would be:
Well, on the wiki you can still use the power sets to transcend layers at H1-A or 0, Which means you can say that
0-innaccessible is baseline H1-A, P(0-innaccessible) is 1 layer in H1-A and P(P(0-innaccessible)) is 2 layers in H1-A, If you repeat this power set operation infinite times, you can go to the infinite layer in H1-A, but as in 1-A and H1-A, it is not enough just transcend infinite layer to reach tier 0.
For tier 0 you have to transcend this whole 0-innaccessible hierarchy in an inaccessible way. To explain this better, if you define λ as a cardinal in any 0-innaccessible hierarchy, whenever we have λ<κ there is 2^λ < κ, so here no matter how big you make λ, it will still be smaller than κ.
This helped thanks
 
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