All Questions
3 questions
20
votes
2
answers
1k
views
Can There be a 1 dimensional Banach-Tarski paradox in the absence of choice
Let $\mathbb{R}$ act on itself by translation. Then there is no finite decomposition of a unit interval into pieces which, when translated, yields two distinct unit intervals.
More formally does ...
- 545
4
votes
1
answer
285
views
Is it compatible with ZF to assume that every amenable discrete group is finite?
The question is in the title, amenability being understood as the existence of a left-invariant finitely additive probability measure on the group of interest. The case of countable groups is treated ...
- 402
11
votes
1
answer
302
views
Without AC, which implications between the different definitions of amenability still hold?
More precisely, I would like to know which implications between the following definitions of amenability of a discrete countable (or even finitely generated) group can be proved to hold with only ZF (...
- 402