The Metahyperchain

The Metahyperchain is a hyperchain, that is, it contains infinite chains. It's size is comparable to The Super Space in Miner's chain.

It starts off with the Metamöbiverse, and because the chain has an infinite number of infinite chains, it doesn't end.

Members of the hyperchain
Here are the members of the chain, in order:

First Layer

 * Metamöbiverse
 * Metakleinverse
 * Metaonerusverse
 * Metahencentroverse
 * Metatworusverse
 * Metatrirusverse
 * Metatorukuverse
 * Metatoruchain
 * Metaonerukuverse
 * Metatworukuverse
 * Metatrirukuverse
 * Metatrirukuverse

Second Layer

 * Metametatoriverse
 * Metatorubarrier
 * Metametamöbiverse
 * Metametakleinverse
 * Metametaonerusverse
 * Metametatorukuverse
 * Metametatoruchain
 * Metametaonerusverse
 * Metametaonerusverse

Third Layer

 * Metametametatoriverse
 * Metametatorubarrier
 * Metametametamöbiverse
 * Metametametatorukuverse
 * Metametametatoruchain
 * Metametametatoruchain

Fourth Layer

 * Metametametametatoriverse
 * Metametametametatorukuverse
 * Metametametametatorukuverse

Fifth Layer and onward

 * Metametametametametatoriverse
 * Metametametametametametatoriverse
 * Metametametametametametatoriverse

Layers of infinity
In the list of members, you can see that the members are grouped into 'layers'. This isn't a mistake, because second layer and onward, the next metametameta...metametatoriverse is MUCH larger than the last, eventually approaching cardinality $$\alef_1$$, or ordinality $$\Omega$$.

Here are some of the sizes for the starts of layers:

Metamöbiverse: $$\epsilon_1$$ (this is the one outlier).

Metametatoriverse: $$\phi(1,0,0)$$

Metametametatoriverse: $$LVO$$or$$\psi(\Omega^{\Omega^\Omega})$$

Metametametametatoriverse: $$BHO$$ or $$\psi(\epsilon_{\Omega+1})$$or$$\psi(\Omega_2)$$

Metametametametametatoriverse: $$\psi(I)$$

...

etc.