Timeline for Does "$X \not\to (\omega)^\omega_2$ for every infinite $X$" imply ${\sf AC}$?
Current License: CC BY-SA 4.0
21 events
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| Apr 14, 2022 at 9:43 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
forgot [] in 2 places
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| Apr 12, 2022 at 13:23 | comment | added | Goldstern | @EmilJeřábek As bof points out implicity in his note, the statement $a\to (b)^e_c$ implies all variants where you increase the number on the left side, or decrease anything on the right side. Also, the exponent $e$ denotes the size (or order type) of the tuples you are considering, which should be easy to remember. | |
| Mar 29, 2022 at 8:12 | vote | accept | Dominic van der Zypen | ||
| Mar 29, 2022 at 3:59 | answer | added | Andrés E. Caicedo | timeline score: 11 | |
| Mar 24, 2022 at 0:44 | comment | added | bof | If only cardinal and ordinal numbers were under consideration, we could just define $(b)^r_k$ to be the corresponding "Ramsey number" and then we could write $a\ge(b)^r_k$ or $a\lt(b)^r_k$ instead of $a\to(b)^r)_k$ or $a\not\to(b)^r_k$. | |
| Mar 23, 2022 at 9:25 | comment | added | მამუკა ჯიბლაძე | @ToddTrimble After so much input, I think, rather than quitting the thread, you are obliged to propose an alternative notation :P | |
| Mar 23, 2022 at 8:01 | comment | added | Emil Jeřábek | Compact it is, but for the life of me I can’t remember which number in the notation denotes which parameter. | |
| Mar 23, 2022 at 6:54 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
added 48 characters in body
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| Mar 21, 2022 at 22:13 | comment | added | Andrés E. Caicedo | Why all this bad publicity? It is useful, and compact. No one who works in the field gets confused. | |
| Mar 21, 2022 at 20:42 | comment | added | Todd Trimble | @Burak Yeesh! No doubt that would be even worse, since it's now insiders who can get confused. Mathematicians are sometimes just really bad (irreflective) about choosing terminology and notation. I guess the same is true in every sphere of life (time for me to quit this thread, I think). | |
| Mar 21, 2022 at 19:54 | comment | added | Burak | @ToddTrimble: Let me add that the very same notation has a different meaning if you use ordinals instead of cardinals in its slots, which can cause more problems than possible confusion with arrows for functions. Nevertheless, it has been around since (at most) 1953 and is widely used, which means that people probably will keep using it. (This is the earliest use of this notation that I could find: londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/jlms/…) | |
| Mar 21, 2022 at 18:51 | comment | added | Todd Trimble | @AndrésE.Caicedo Never!! :-) | |
| Mar 21, 2022 at 18:41 | comment | added | Dominic van der Zypen | Brilliant, thanks @ToddTrimble! It seems to me that the use of "Egad" is less common than denoting a property with $\to$ and $\not\to$ respectively. (Just kidding.) | |
| Mar 21, 2022 at 18:35 | comment | added | Andrés E. Caicedo | @Todd It grows on you. | |
| Mar 21, 2022 at 18:21 | comment | added | Todd Trimble | @Burak Okay, my apologies for attributing this to you, and I will remove that attribution. (But I am still of the strong opinion that the notation is terrible!) Dominic: merriam-webster.com/dictionary/egad | |
| Mar 21, 2022 at 18:18 | comment | added | Dominic van der Zypen | @Burak --> thanks for your wonderful notes which gave me a great entry point to infinite combinatorics!! | |
| Mar 21, 2022 at 18:18 | comment | added | Dominic van der Zypen | @ToddTrimble I have encountered the notation so many times that I am quite certain that it is standard in that field. For instance Saharon Shelah uses it in many articles. (By the way, I didn't find what "Egad" stands for, I took it to be an abbreviation like "WLG") | |
| Mar 21, 2022 at 17:46 | comment | added | Burak | As the author of the notes, I tried to use the standard notation (known as the Erdös-Rado arrow notation) instead of inventing a new notation. | |
| Mar 21, 2022 at 16:52 | comment | added | Todd Trimble | Egad, that is bad notation. I find it quite perverse to use the arrow notation both for a structure (a function: the usual notation) and for a property. I quite failed to understand at first that $\not \to$ meant failure of that property. | |
| Mar 21, 2022 at 13:47 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
clarified question and swapped ) and . in second-to-last paragraph
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| Mar 21, 2022 at 10:28 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |