Timeline for "Matryoshka" sets and the Axiom of Choice
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 10, 2021 at 7:29 | comment | added | Dominic van der Zypen | Seems I have to brush up on my negation / contraposition handling :) | |
| Jul 9, 2021 at 22:32 | comment | added | Asaf Karagila♦ | Again, you're making the wrong inference. All it shows is that there are witnesses for Mat₁ which are not witnesses for Mat₂. But the statement of both of the Mat's is existential. It quantifies over all sequences in the universe. | |
| Jul 9, 2021 at 18:57 | comment | added | Dominic van der Zypen | Thanks! So $\neg$(Mat_1) is stronger than $\neg$(Mat_2), and is it known about any implication of these to the Partition Principle, or the Boolean Prime Ideal Theorem? | |
| Jul 9, 2021 at 15:11 | comment | added | Asaf Karagila♦ | See mathoverflow.net/questions/308095/… and mathoverflow.net/questions/308030/… | |
| Jul 9, 2021 at 14:07 | comment | added | Dominic van der Zypen | Thanks @AsafKaragila for your comment; sorry for being slow, can you give me a hint? I am especially interested in your "uniqueness" remark | |
| Jul 9, 2021 at 14:06 | comment | added | Dominic van der Zypen | Thanks @Wojowu for both the link and your additional comment | |
| Jul 9, 2021 at 13:51 | comment | added | Wojowu | I've just realized there is a subtle difference between this question and the one I linked above - essentially, in this question, you need to not only have a descending sequence of cardinals, but you also need to choose the representatives of cardinalities. Because of this it is for instance not immediate that the negation of Mat_1 implies there are no infinite Dedekind-finite cardinals (while it would be clear if we looked at cardinals themselves). | |
| Jul 9, 2021 at 12:34 | comment | added | Asaf Karagila♦ | It's very easy to find examples of sequences witnessing (1) but not (2), but it's a lot harder to show that there are no other sequences. | |
| Jul 9, 2021 at 12:06 | comment | added | Wojowu | math.stackexchange.com/q/1634372/127263 | |
| Jul 9, 2021 at 12:01 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |