Timeline for A different ordering on ${\cal P}(\omega)$
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 24, 2017 at 12:32 | vote | accept | Dominic van der Zypen | ||
| Oct 24, 2017 at 6:21 | comment | added | Dominic van der Zypen | Right - sorry for the buggy definition! That's a nuisance if the OP doesn't get it right -- I apologise | |
| Oct 24, 2017 at 1:09 | comment | added | Nik Weaver | Comments that begin "Maybe I'm just confused" are the most dangerous ones, aren't they? Well, you are right, I totally misread the question. Though I wonder if the definition I used was actually the intended one, since otherwise the problem is trivial. | |
| Oct 23, 2017 at 22:28 | comment | added | Andreas Blass | Maybe I'm just confused, but it seems to me that your isomorphism between $\leq_{\text{inj}}$ and the coordinatewise order on functions $\omega\to\omega$ involves $\leq_{\text{inj}}$ defined as "there is an injective order-preserving $f:\omega\to\omega$ with $f(A)=B$", whereas the definition in the question ends with $f(A)\subseteq B$. With the $\subseteq$ version of the definition, it seems that every subset of $\omega$ is $\leq_{\text{inj}}$ every infinite subset of $\omega$. | |
| Oct 23, 2017 at 14:33 | vote | accept | Dominic van der Zypen | ||
| Oct 24, 2017 at 6:20 | |||||
| Oct 23, 2017 at 13:56 | history | edited | Nik Weaver | CC BY-SA 3.0 |
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| Oct 23, 2017 at 13:43 | history | edited | Nik Weaver | CC BY-SA 3.0 |
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| Oct 23, 2017 at 13:25 | history | edited | Nik Weaver | CC BY-SA 3.0 |
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| Oct 23, 2017 at 13:19 | history | answered | Nik Weaver | CC BY-SA 3.0 |