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
3 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 13, 2012 at 0:59 | comment | added | Patrick Reardon | Perhaps I'm missing something here. The game ends at a countable stage so pR's plays from $R\setminus C$ won't produce an injection from $\omega_1$ to $R$. If we need a more precise strategy, what about this? We may assume that the injective copy of pN's set is the set of positive integers $P$. For each turn $n<\omega$, pR plays -n. At every turn after that, pR plays the continued fraction defined by all previous plays of pN. | |
| Feb 11, 2012 at 3:32 | comment | added | François G. Dorais | You need some choice to keep picking numbers from R-C. Even if R-C is uncountable, I don't know how to write a strategy without an injection from $\omega_1$ into R-C, whose existence is not provable in plain ZF. | |
| Feb 11, 2012 at 1:06 | history | answered | Patrick Reardon | CC BY-SA 3.0 |