>>11289624In what sense? Anyway, the answer is most certainly no.
Here's a few pointers:
, or , is a countable ordinal in the smaller to medium range.
You can describe the order type it represents in Peano arithmetic.
It represents, roughly, the collection of all arbitrary sized but finite lists whos entries are natural numbers.
As a countable ordinal, it's cardinality is that of the natural numbers, .
Consider the description of countable ordinal types beyond infinity here:
https://youtu.be/EAAC9dCV9_k is of size of the continuum,
and where is set holding all countable ordinals, i.e. the smallest uncountable ordinal. This one is uncountable, so long long past all the easily compresensible ordinals.
To make the comparison sharp, , is to claim the continuum hypothesis.
The size of w.r.t. to ordinals is independent of ZFC, there's no good answer to it.
So your question was doomed from the start...
>It seems though like that definition might be a special case of some stuff like topos or sheaves or something.What is "that definition" in this sentence now? Sheaf-categories fulfill those properties, so the latter is the more general variant, for what it's worth.
I just wanted to point you to it, in case you're interested. I was a bit scared of looking at your formulas.
>Has analysis, algebra, topology etc. just already "filled" the space of possible mathematical definitions?"No", but I think it's a matter of (Kolmogorov) complexity.
