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3 votes
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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 $\...
Brendan McKay's user avatar
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 ...
Dominic van der Zypen's user avatar