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Martin Sleziak
Martin Sleziak
8:56 AM
specific-question Again, to me infinite-combinatorics seems to be a good fit for questions dealing with MAD families. MAD families on $\kappa>\omega$
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Q: MAD families on $\kappa>\omega$

Dominic van der ZypenLet $\kappa>\omega$ be a cardinal. We say that ${\cal A}\subseteq{\cal P}(\kappa)$ is an almost disjoint family if $|A|=\kappa$ for $A\in{\cal A}$, and $|A\cap B|<\aleph_0$ for $A\neq B\in{\cal A}$. Zorn's Lemma implies that every almost disjoint family is contained in a maximal such family, whic...

set-theory lo.logic
 
 
2 hours later…
YCor
YCor
10:51 AM
@MartinSleziak Yes!
 
Martin Sleziak
Martin Sleziak
specific-question Online courses for mathematics. I see that it was retagged. Most likely the OP entered discrete-mathematics - and the existing synonym changed it to co.combinatorics. The OP explicitly mentions: " in particular discrete mathematics, calculus, and linear algebra".
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Q: Online courses for mathematics

Ansel LimI'm sorry if I'm posting this in the wrong forum. My background is in biology and medicine. I am looking to re-learn undergraduate-level mathematics, in particular discrete mathematics, calculus, and linear algebra. I did do these courses back in college, but I've since forgotten most of this. Do...

mathematics-education gm.general-mathematics online-resources
I will not be surprised if that question gets closed - it is currently sitting in the close votes review.
I have added infinite-combinatorics to the question about MAD families. It seems that questions is being edited to clarify the terminology.
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Q: Families with finite intersection property on $\kappa>\omega$

Dominic van der ZypenLet $\kappa>\omega$ be a cardinal. We say that ${\cal A}\subseteq{\cal P}(\kappa)$ has the finite intersection property (FIP) if $|A|=\kappa$ for $A\in{\cal A}$, and $|A\cap B|<\aleph_0$ for $A\neq B\in{\cal A}$. For which cardinals $\kappa>\omega$ is there a family with FIP ${\cal A}\subseteq {\...

set-theory lo.logic infinite-combinatorics
Did you mean to write $|A\cap B|<\aleph_0$ for $A\neq B$? AFAIK, this is not the usual definition. — Hannes Jakob 2 hours ago
I did not mean to write $|A\cap B|<\kappa$ if that is what you had in mind? Maybe I have to change my terms from "almost disjoint" to "finite intersection" families. Will edit - thanks for your comment @HannesJakob — Dominic van der Zypen 2 hours ago
“Almost disjoint” is correct (though it is used with several variant meanings). “Finite intersection property” is something completely different: a family of sets has the FIP if every finite subfamily has nonempty intersection. — Emil Jeřábek 1 hour ago
2 days ago, by Martin Sleziak
@YCor You can check out the overview of tag-related terminology I wrote at the end of this post: What to do with the synonyms for the deprecated tags?
@YCor Is the explanation of tag-merging (and other related terms) in the linked post sufficient for what you needed?
 
YCor
YCor
@MartinSleziak yes it was already clear. In a sense, I tend to regret that peano-arithmetic cannot be recreated, as it seems more focussed than theories-of-arithmetic. My favourite option would have been that theories-of-arithmetic be added to each peano-tagged question (if there's room for additional tag). But it seems in conflict with Emil Jerabek's opinion and I don't want to propose too many conflicting options. We converge to synonym, at least if mods accept to contribute.
 
Martin Sleziak
Martin Sleziak
Ok. Thanks for the response! I am glad that at least the technical aspects are clear.
Of course, the specifics of these particular tags are for discussion.
I assume you mean the synonym in the direction peano-arithmetic $\to$ theories-of-arithmetic, i.e., with theories-of-arithmetic as the master tag, right?
What about models-of-pa, that tag should stay separate?
I see that there is a separate tag bounded-arithmetic - which I did not notice until now.
Would Category:Formal theories of arithmetic on Wikipedia be a reasonable approximation of the intended content of theories-of-arithmetic tag?
The tag-excerpt says at the moment: "Theories of arithmetic in first-order logic, such as Peano arithmetic, second-order arithmetic, Heyting arithmetic, and their subsystems and extensions."
 
 
12 hours later…
YCor
YCor
11:39 PM
models-of-pa has only 9 questions, it should be renamed or replaced but this can be done manually.
@MartinSleziak yes, this seems to quite well match (from my exterior point of view)
I guess it should also include, by extension, algebraic structures based modeling arithmetic axioms, such as Heyting algebras.
 

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