Skip to main content
1 of 5
Joel David Hamkins
  • 236.3k
  • 44
  • 777
  • 1.4k

The statement (**) is inconsistent with ZFC, because my answer to your previous question shows that even the finitary form is inconsistent. There is a coloring of countable ordinals, such that for no ordinals $\alpha,\beta$ do the ordinals $\alpha+\beta\cdot\omega$ and $\alpha+\beta\cdot\omega^2$ get the same color.

Joel David Hamkins
  • 236.3k
  • 44
  • 777
  • 1.4k