Timeline for Creating tag "small-uncountable-cardinals"
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Mar 14, 2019 at 9:27 | comment | added | bof | precisely $\le\mathfrak c$. On the other hand, from the words "cardinal characteristics" it's not clear to us people in the street that it's not about cardinal invariants of topological spaces, or Boolean algebras, or Abelian groups, or anything at all. | |
| Mar 14, 2019 at 9:25 | comment | added | bof | I have to take your word for it that the experts on set theory prefer "cardinal characteristics" to "small uncountable cardinals" but I don't understand it. Why "characteristics"? What does this use of "characteristics" have to do with any other mathematical or non-mathematical use of the word? At least the meaning of "small uncountable cardinals" is related in an obvious way to the meanings of the three words. (Historically I guess it comes from Hechler's 1972 paper "A dozen small uncountable cardinals".) Of course it's not clear from the words "small uncountable cardinals" that "small" means | |
| Mar 13, 2019 at 5:35 | comment | added | David Roberts Mod | Yes, we get questions on this site about "algebraic geometry" which are really <--- like questions at the level of elementary undergrad proofs which are tagged [formal-proof]... | |
| Mar 12, 2019 at 21:08 | comment | added | Andrés E. Caicedo | @YCor For instance, $\mathfrak b$, the unbounded number, is the least cardinality of an unbounded subset of $\mathbb N^{\mathbb N}$ under the relation $f\le^* g\Longleftrightarrow \exists n\,\forall m>n\, f(m)\le g(m)$. | |
| Mar 12, 2019 at 21:08 | comment | added | YCor | Got it: en.wikipedia.org/wiki/Cardinal_characteristic_of_the_continuum. This will lead anyway, to numerous confusions. I also thought of algebraic geometry, but you probably know that algebraic geometry is by far a broader, more important and older subject, and a whole subfield of math. | |
| Mar 12, 2019 at 21:08 | comment | added | Andrés E. Caicedo | @YCor Not the people for which the tag is intended. Yes, we get questions on this site about "algebraic geometry" which are really about finding the equation of a line going through two points whose coordinates are given. This does not mean "algebraic geometry" is a useless tag. Classically, cardinal characteristics or cardinal invariants are cardinals $\kappa$ whose definition implies $\aleph_0<\kappa\le 2^{\aleph_0}$. In practice, they are defined in terms of combinatorial properties. | |
| Mar 12, 2019 at 20:58 | comment | added | YCor | I'm thinking of "characteristic" in the vulgar sense, in the same way as "cardinal features". What is meant by cardinal characteristics? Anyway, if there's a precise sense and my "vulgar" interpretation is mistaken, I guess others will do the same mistake too. | |
| Mar 12, 2019 at 20:57 | comment | added | Andrés E. Caicedo | @YCor No, that sounds crazy. "Cardinal characteristic" is a specific thing with specific meaning. "Large cardinals" means something else. It is like saying that a tag "Euclidean geometry" would encompass "Artificial intelligence". | |
| Mar 12, 2019 at 20:55 | comment | added | YCor | OK, so I maintain my previous comment: cardinal-characteristics would encompass the quite broad large-cardinals and this is at odds with the given proposal, if I understand correctly. | |
| Mar 12, 2019 at 20:53 | history | edited | Andrés E. Caicedo | CC BY-SA 4.0 |
added 316 characters in body
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| Mar 12, 2019 at 20:51 | comment | added | Andrés E. Caicedo | @YCor No, I think that "small countable cardinals" is too vague in scope to be useful. Cardinal characteristics are specific objects and the examples suggested by Taras seem all to be about them. | |
| Mar 12, 2019 at 20:39 | comment | added | YCor | It seems I was confused by your answer, and thought you suggested cardinal-characteristics as better than small-uncountable-cardinals. If you think that creating small-uncountable-cardinals is a good idea, maybe it would have been a good starting point. | |
| Mar 12, 2019 at 20:34 | comment | added | Andrés E. Caicedo | I am confused by this comment. Why would one think that small uncountable cardinals is meant to encompass large cardinals? It is the same confusion I feel when reading your proposal. The tag CH is certainly not meant to encompass situations where CH fails. | |
| Mar 12, 2019 at 20:04 | comment | added | YCor | There are two things in small-uncountable-tags that would be unclear in a cardinal-characteristics: first, it would encompass large cardinals, and there's already the tag large-cardinals which is much bigger than the previous two ones (currently 498 questions). Second, it might be misused for counting problems finite combinatorics. | |
| Mar 12, 2019 at 17:17 | history | answered | Andrés E. Caicedo | CC BY-SA 4.0 |