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Transcending Berkeley. Can Tier be scaled?
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Question About Berkeley Cardinal
- Thread starter Sasukesama0492
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Assume that the Berkeley Cardinal is actually tied to the cosmology size, transcending this cardinal is very high into tier 0, baseline tier 0 is Mahlo Cardinal and Berkeley Cardinal is far exceed Mahlo
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First, Do not speak Turkish on this wiki.
Second, The example you gave for Woodin is already a separate absurdity.
This is also wrong actually.
Anyway, let me explain a little bit with VSBW logic, I won't take too long.
In the Vsbw system, they find even qualitative transcendence is enough for the layers on H1-A, mathematically speaking, I mean that, if k is an inaccessible cardinal, P(k) naturally becomes 1 layer in H1-A.
Well, if you follow this logic, what is completely inaccessible for the H1-A hierarchies will be 1-inaccessible.
When we continue, even 2-inaccessible will be inaccessible for any 0 hierarchies and will also get an inaccessible layer on 0.
So even infinite^infinite^infinite^infinite^infinite^infinite... layer will still technically be smaller than this.
Mahlo would then again be inaccessible for any 0 hierarchy but Mahlo is also way beyond it.
My recommendation is to use the phrase Mahlo gets as many layers as Mahlo in tier 0 for situations like this.
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