Timeline for Does every non-empty set admit a group structure (in ZF)?
Current License: CC BY-SA 3.0
17 events
| when toggle format | what | by | license | comment | |
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| S Dec 10, 2015 at 19:00 | history | suggested | David Zhang | CC BY-SA 3.0 |
Improved LaTeX formatting (in particular, changed $o$ to $\circ$ to denote group operation)
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| Dec 10, 2015 at 18:47 | review | Suggested edits | |||
| S Dec 10, 2015 at 19:00 | |||||
| Oct 10, 2015 at 7:03 | comment | added | Péter Komjáth | Hajnal now loaded his paper with Kertesz to Reseacrhgate, so it's available: researchgate.net/publication/… | |
| Jun 13, 2010 at 17:29 | comment | added | Péter Komjáth | I have it. Same proof. | |
| Feb 1, 2010 at 4:47 | history | edited | Mike Shulman | CC BY-SA 2.5 |
group structures only exist on nonempty sets (-:
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| Jan 26, 2010 at 21:36 | comment | added | Konrad Swanepoel | I think this proof is Hajnal and Kertesz'. Some indirect evidence via Google: in these lecture notes on set theory on the web (in German) users.math.uni-potsdam.de/~raesch/logik/Seminarbericht.pdf on pages 36-37 the same proof occurs. The only reference there is to the paper of Hajnal and Kertesz. Somebody with access to this paper out there? | |
| Jan 26, 2010 at 19:30 | comment | added | Ashutosh | I don't know. I cannot access that paper either. | |
| Jan 26, 2010 at 19:18 | comment | added | Joel David Hamkins | Is it the same proof? My personal subscription to Publ. Math. Debrecen here at home unfortunately runs out in 1971... | |
| Jan 26, 2010 at 15:08 | comment | added | Ashutosh | I did some googling and found this: Hajnal, A., Kertész, A. - Some new algebraic equivalents of the axiom of choice, Publ. Math. Debrecen 19 (1972), 339--340 (1973). Review on MathSciNet: The authors show that in ZF, the axiom of choice is equivalent to the statement: on every nonempty set there exists a cancellative groupoid. | |
| Jan 26, 2010 at 14:48 | comment | added | Ashutosh | I had heard this problem from a friend. We were trying to determine the possible sizes (cardinal types) of groups in a choice free world and ended up with something of this kind. I'm sure it's a folklore result but cannot be sure. I'll try asking him. | |
| Jan 26, 2010 at 13:20 | comment | added | Joel David Hamkins | Ashutosh, is this your argument? I want to use it and give proper credit. | |
| Jan 26, 2010 at 8:22 | vote | accept | Konrad Swanepoel | ||
| Jan 26, 2010 at 8:20 | comment | added | Konrad Swanepoel | Aha, very neat! | |
| Jan 26, 2010 at 0:21 | history | edited | Ashutosh | CC BY-SA 2.5 |
added 4 characters in body; deleted 4 characters in body
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| Jan 26, 2010 at 0:15 | history | edited | Ashutosh | CC BY-SA 2.5 |
deleted 22 characters in body; added 22 characters in body; added 4 characters in body
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| Jan 26, 2010 at 0:13 | comment | added | Joel David Hamkins | Fantastic! This is a great argument! It is just equivalent to AC. | |
| Jan 26, 2010 at 0:07 | history | answered | Ashutosh | CC BY-SA 2.5 |