- #1

jose diez

- 3

- 0

(*) if A≈B & C≈D & A∩C=∅ & B∩D=∅ then A∪C≈B∪D

It seems intuitive that if one replaces the strong

A∩C=∅ & B∩D=∅

condition by the weaker

A∩C≈B∩D

the implication

(**) if A≈B & C≈D & A∩C≈B∪∩D then A∪C≈BD

still holds.

(**) does not seem to be much stronger than (*), nevertheless I have been able to prove (**) only using Ax of Choice (ACh). This suggested to me that (**) might be other equivalent to ACh, but I have not found it in the standard lists, nor I have been able to prove that (**) implies ACh.

Does anybody have any clue on this?