Answer by Burak for Is it possible to formulate the axiom of choice as the...
This is related to Nate Eldredge's answer that shows some amount of choice is required. In the case $G=\mathbb{N}$, $\kappa = \omega_0$ and $C=2$, the equivalence relation you define is eventual...
View ArticleAnswer by godelian for Is it possible to formulate the axiom of choice as the...
The question makes sense when $\kappa=\aleph_0$ since the statement involves no choice. But according to the interesting book by Hardin and Taylor, "The mathematics of coordinated inference" (2013),...
View ArticleAnswer by Nate Eldredge for Is it possible to formulate the axiom of choice...
It is certainly true that some choice is required.An isomorphic game (mapping (giraffes, scarves, lion) to (prisoners, hats, warden)) was considered by Hardin and Taylor in their stimulating (and...
View ArticleAnswer by Joel David Hamkins for Is it possible to formulate the axiom of...
Here is one interesting observation:If the giraffes form an amorphous set, which is an infinite set all of whose subsets are either finite or co-finite, then they have a winning strategy in the case...
View ArticleIs it possible to formulate the axiom of choice as the existence of a...
Consider the following situation:There is an infinite set $G$ of giraffes. A lion comes and announces a set $C$ of all possible colours and an infinite cardinal $\kappa$. The hungry lion tells the...
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