Timeline for Is there any infinite set which is Dedekind finite and weakly Dedekind finite?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| May 26, 2016 at 17:21 | comment | added | Asaf Karagila♦ | I just answered that two comments ago. | |
| May 26, 2016 at 17:20 | comment | added | Jaruwat Rodbanjong | OK. But in the second question, is power set of X is weakly Dedekind infinite? (In my class, amorphous means cannot be decomposed into two infinite set.) | |
| May 26, 2016 at 17:11 | comment | added | Asaf Karagila♦ | No. An amorphous set is always weakly Dedekind finite; but in Cohen's first model there are no infinite weakly Dedekind finite sets. | |
| May 26, 2016 at 17:05 | comment | added | Jaruwat Rodbanjong | You mean that "an amorphous set, in Cohen's first model, is infinite & Dedekind finite & weakly Dedekind finite", right? | |
| May 26, 2016 at 16:54 | comment | added | Asaf Karagila♦ | Yes, as I wrote. And as I wrote in my answer, if $X$ is infinite (Dedekind finite or not), then $\mathcal P(X)$ can be mapped onto $\omega$. | |
| May 26, 2016 at 16:51 | comment | added | Jaruwat Rodbanjong | In my class, a set X is weakly Dedekind finite if there is no surjection from X onto $/omega$. | |
| May 26, 2016 at 16:46 | comment | added | Asaf Karagila♦ | Weakly Dedekind finite sets, if my memory serves me right (and you provided no definition) are Dedekind finite sets that cannot be mapped onto $\omega$. | |
| May 26, 2016 at 16:44 | comment | added | Jaruwat Rodbanjong | Sorry, but i want to know whether P(X) is "weakly" Dedekind finite or not, not Dedekind finite. | |
| May 26, 2016 at 14:08 | comment | added | Jaruwat Rodbanjong | Oh, you made my day. Thank you so much :) | |
| May 26, 2016 at 13:54 | history | answered | Asaf Karagila♦ | CC BY-SA 3.0 |