All Questions
2 questions
3
votes
0
answers
176
views
Ramsey's infinite principle and the axiom of choice
Frank Plumpton Ramsey, best known for giving his name to Ramsey Theory, presented the following theorem in On a Problem of Formal Logic, that was submitted in 1928 and published posthumously.
Let $\...
9
votes
1
answer
513
views
Does "$X \not\to (\omega)^\omega_2$ for every infinite $X$" imply ${\sf AC}$?
For any set $X$ and cardinal $\mu \neq \emptyset$, we denote by $[X]^\mu$ the collection of subsets of cardinality $\mu$. If $\kappa, \mu \neq \emptyset$ are cardinals and $f: [X]^\mu\to \kappa$ is a ...