All Questions

As far as I know, the only way we currently know how to prove Borel determinacy in $\mathsf{ZFC}$ is to go through unravelability (a rather technical property whose definition can be found in Martin's ...

So this is an embarrassing question. Call a preorder $\mathbb{P}$ good if it has the following properties: Every countable chain in $\mathbb{P}$ has a least upper bound. $\mathbb{P}$ is directed (any ...

Axiom of choice arranges all cardinalities into a well-ordered chain but without it their ordering can be wild in general ZF models, e.g. two cardinalities may not even have inf or sup. However, ...