Timeline for Set Cardinality Game - Can a player with numbers in R win over a player with numbers in N as each of them in one turn has to present a new number?
Current License: CC BY-SA 3.0
12 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
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| Feb 11, 2012 at 1:06 | answer | added | Patrick Reardon | timeline score: 1 | |
| Feb 7, 2012 at 8:42 | vote | accept | Dávid Natingga | ||
| Feb 6, 2012 at 9:43 | answer | added | Jirka Hanika | timeline score: 1 | |
| Feb 5, 2012 at 16:39 | comment | added | François G. Dorais | @Ramiro: pN still can't win because she will exhaust all of N by herself in some countable ordinal number of steps. If pN plays first on limit rounds, then pR can just wait the game out copying pN's moves using an injection from pN's countable set into $\mathbb{R}$. If pR plays first on limit rounds, then it's less clear what happens. It's probable that a winning strategy for pR gives an injection from $\omega_1$ into $\mathbb{R}$, but that's not entirely clear to me right now. | |
| Feb 5, 2012 at 16:29 | comment | added | Ramiro de la Vega | What if pN plays with a countable set not containing any real and they are playing in a universe where there is no subset of the reals of size $\aleph_1$? | |
| Feb 5, 2012 at 15:19 | comment | added | Dávid Natingga | Yes, they are reals, thank you for pointing out I can use $\LaTeX$. So if I understand, in general p$\aleph_N$ with a set A can be defeated by another player whose set is a superset of A in $\omega_N+1$ steps? | |
| Feb 5, 2012 at 14:58 | history | edited | Dávid Natingga | CC BY-SA 3.0 |
added 279 characters in body; added 56 characters in body
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| Feb 5, 2012 at 14:40 | comment | added | François G. Dorais | None of the players can win in $\omega$ steps or fewer. With $\omega+1$ steps, pN's opponent can always win by choosing the first available natural number at each round, exhausting N in $\omega$ steps. | |
| Feb 5, 2012 at 14:36 | comment | added | François G. Dorais | What is R, the reals? How long is the game? Longer than $\omega$ steps, I suppose? (You can use $\LaTeX$ expressions by enclosing in dollar signs.) | |
| Feb 5, 2012 at 14:31 | history | edited | Dávid Natingga | CC BY-SA 3.0 |
edited tags; edited title
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| Feb 5, 2012 at 14:23 | history | asked | Dávid Natingga | CC BY-SA 3.0 |