Skip to main content
2 of 4
deleted 67 characters in body
Joel David Hamkins
  • 236.3k
  • 44
  • 777
  • 1.4k

Your principle TC implies the rigid relation principle RR, a weak choice principle introduced by Justin Palumbo and myself in this paper:

The rigid relation principle is the assertion that every set admits a rigid binary relation. This is true under TC, since $\langle X,\in\rangle$ is rigid whenever $X$ is a transitive set, and so every set that is bijective with a transitive set admits a rigid binary relation.

Meanwhile, Justin and I proved that RR is strictly intermediate between ZF and ZFC.

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