2
votes
2answers
79 views

Formal approach to (countable) prisoners and hats problem.

I've found this nice puzzle about AC (I'm referring to the countable infinite case, with two colors). The puzzle has been discussed before on math.SE, but I can't find any description of what is ...
9
votes
0answers
185 views

Paradoxical models of $\sf ZF$ without choice [closed]

There are some models of $\sf ZF$ without the Axiom of choice, where some paradoxical statements hold that are not possible in $\sf ZFC$ (we do not require that all those statements necessarily hold ...
5
votes
0answers
66 views

Connectedness of parts used in the Banach–Tarski paradox

A quote from the Wikipedia article "Axiom of choice": One example is the Banach–Tarski paradox which says that it is possible to decompose the 3-dimensional solid unit ball into finitely many ...
5
votes
2answers
169 views

reverse Banach-Tarski paradox

Is it possible to reverse the operation of the Banach-Tarski paradox? That is, I have two three-dimensional balls, and is it possible to combine them into one ball that is identical to one of the ...