Given the discussion, I tend to be gradually convinced that creating small-uncountable-cardinals is a good idea, and a good counterpart to the existing quite broad large-cardinals, which currently has almost 500 occurrences. I initially expressed that all this could be embedded into continuum-hypothesis, but several people have argued against this and I'm fine with those arguments. I'd like, anyway, that one additional benefit of the discussion would be to clarify the role/meaning of the tag infinite-combinatorics; I don't think it's a separate issue as the intersection is significant.

Also, I'm against cardinal-characteristics,

• because this will result in a misunderstanding of the its meaning (will be misused at many occasions), as it will be widely understood as "properties of cardinals", and I don't think that properly understanding the meaning of a tag should be a privilege for those very specialists of the given subjects,

• because "characteristics" seems to be used only by a proper subcommunity among the people dealing with such cardinals (I can substantiate this claim upon request), so a few questions naturally fitting with this tag will not be tagged so (or later by other people) — a typical such tag in another area seems to be calculus-of-variations.

• because the restriction to be $\le 2^{\aleph_0}$ makes it too restrictive. Cardinals such as $(2^{\aleph_0})^+$ or $2^{2^{\aleph_0}}$ should be considered as small, as opposed to large cardinals. Small/large is not a completely defined boundary (roughly, large would be at least the smallest inaccessible) but I don't think it's not a problem, and it's even better than setting artificial boundary.

• because I can't detect any sensible argument making it better than small-uncountable-cardinals.

Given the discussion, I tend to be gradually convinced that creating small-uncountable-cardinals is a good idea, and a good counterpart to the existing quite broad large-cardinals, which currently has almost 500 occurrences. I initially expressed that all this could be embedded into continuum-hypothesis, but several people have argued against this and I'm fine with those arguments. I'd like, anyway, that one additional benefit of the discussion would be to clarify the role/meaning of the tag infinite-combinatorics; I don't think it's a separate issue as the intersection is significant.

Also, I'm against cardinal-characteristics,

• because this will result in a misunderstanding of the its meaning (will be misused at many occasions), as it will be widely understood as "properties of cardinals", and I don't think that properly understanding the meaning of a tag should be a privilege for those very specialists of the given subjects,

• because "characteristics" seems to be used only by a proper subcommunity among the people dealing with such cardinals (I can substantiate this claim upon request), so a few questions naturally fitting with this tag will not be tagged so (or later by other people) — a typical such tag in another area seems to be calculus-of-variations.

• because the restriction to be $\le 2^{\aleph_0}$ makes it too restrictive. Cardinals such as $(2^{\aleph_0})^+$ or $2^{2^{\aleph_0}}$ should be considered as small, as opposed to large cardinals. Small/large is not a completely defined boundary (roughly, large would be at least the smallest inaccessible) but I don't think it's not a problem, and it's even better than setting artificial boundary.

• because I can't detect any sensible argument making it better than small-uncountable-cardinals.

Edit (April 2020)

Finally a majority led to create cardinal-characteristics about 13 months ago, with at this date 38 questions including 10 older ones that were retagged.

The use of this tag seems consistent and I'm finally convinced it was a good idea and that my reluctance was excessive.