Timeline for Infinite games: are they well defined?
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
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| Jul 17, 2010 at 9:32 | comment | added | Wadim Zudilin | Carl, I won't be too critical to Tony's answer: there could be sets $G$ for which wining strategies do not exist. | |
| Jul 16, 2010 at 16:03 | comment | added | Carl Mummert | Each set $G$ leads to a different game. For some sets $G$, the game will be determined (e.g. if $G$ is empty). For other sets, it will not be determined. For example, if $G$ is a "Bernstein set", neither containing nor disjoint from any nonempty perfect closed set, then neither player will have a winning strategy. This is because a winning strategy for player 1 can be used to build a nonempty perfect closed set in $G$, and a winning strategy for player 2 can be used to build a nonempty perfect closed set in the complement. Bernstein sets can be constructed in ZFC using the axiom of choice. | |
| Jul 16, 2010 at 14:56 | history | edited | Tony Huynh | CC BY-SA 2.5 |
added 216 characters in body
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| Jul 16, 2010 at 14:50 | history | answered | Tony Huynh | CC BY-SA 2.5 |