Timeline for Ideals on $\mathbb N$ and large sets that have small intersection
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 5, 2018 at 8:05 | answer | added | KP Hart | timeline score: 3 | |
| Sep 24, 2018 at 6:37 | answer | added | Yifan | timeline score: 1 | |
| Sep 23, 2018 at 14:39 | answer | added | Andreas Blass | timeline score: 4 | |
| Sep 22, 2018 at 19:27 | vote | accept | Tomasz Kania | ||
| Sep 22, 2018 at 19:10 | answer | added | Don Monk | timeline score: 4 | |
| Sep 22, 2018 at 17:45 | answer | added | Jing Zhang | timeline score: 2 | |
| Sep 22, 2018 at 16:54 | comment | added | YCor | By the way this is purely ring-theoretic: in a ring $R$ (say associative unital commutative), you considers ideals $I$ and subsets $\mathcal{A}\subset R\smallsetminus I$ such that for all $a\neq b\in\mathcal{A}$ we have $ab\in I$, and require that all such subsets are countable. In a Boolean algebra $a,b\notin I,a-b\in I$ implies $ab\notin I$, so this forces $\mathcal{A}$ to embed into $A/I$. Beyond the Boolean case, this applies when $A/I$ is reduced. | |
| Sep 22, 2018 at 16:51 | comment | added | YCor | You have all ideals $I$ such that $P(N)/I$ is countable (but this forces $P(N)/I$ finite). | |
| Sep 22, 2018 at 16:51 | history | edited | Tomasz Kania | CC BY-SA 4.0 |
added 17 characters in body
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| Sep 22, 2018 at 16:50 | comment | added | YCor | "only the empty family": you mean "only the empty family or singletons". By the way, what you call "family" is usually called a "subset". Of course, every set can be thought of as a family $(a)_{a\in A}$... | |
| Sep 22, 2018 at 16:38 | history | asked | Tomasz Kania | CC BY-SA 4.0 |