Basic Information[]
Countable Absolute Infinity is the 3rd named Entry after Absolute Infinity in NO! Video 0toATE. It's only definition is that it is larger than Transfinity. It has Definition Index 3.
Discussion[]
The numbers name is a form of word-salad. The term Countable in a Set Theoretic Context means that the elements of a Set (or collection) may be put in one-to-one correspondence with the Set of Counting Numbers. When this can be done, it is said to be equinumerous with them and have a cardinality of ℵ0. This would be strictly smaller than Absolute Infinity, so this suggests "Countable" Absolute Infinity is somehow smaller than Absolute Infinity, when it is clearly intended to be larger.
This demonstrates that NO! was not familiar with Set Theoretic Concepts (at least when 0toATE was created). If however we take a more relaxed view, essentially words added to previous names have the effect of intensifying the original root. So essentially "Countable" here is a arbitary and meaningless adjective that implies it is "more than" Absolute Infinity by definition. Various Adjectives are used to heighten pre-existing Ordinals and Cardinals, such as appending "True", and is "True Epsilon" or "True Absolute Infinity". The exact semantics of this has not been fully analyzed or understood at this time.
As to what this could possibly mean, all we can say is that it is perhaps a much larger Cardinal than Transfinity, or a new kind of Degree of Absoluteness. This concept is itself not very well defined, but it is possible this could be C^4(0) or Perhaps, the Foundation following Absolute Foundation, but still contained within Absolute Incomprehensible.
It's status to the Mathean Absolutes has no canonical answer. It is currently under peer review.