Yes, Caicedo mentions that GCH implies AC. This is a theorem of Siepinski, who proved it locally. Specker strengthened the local statement to CH(S)+CH(2^S) ⇒ S is well-orderable. It is open whether CH(S) ⇒ S is well-orderable.
Ok. That makes sense. I think we’re on the same page then now, and you are correct that Buie and I were confuse about the precise version of the statements in question.
Yes, Caicedo mentions that GCH implies AC. This is a theorem of Siepinski, who proved it locally. Specker strengthened the local statement to CH(S)+CH(2^S) ⇒ S is well-orderable. It is open whether CH(S) ⇒ S is well-orderable.
Ok. That makes sense. I think we’re on the same page then now, and you are correct that Buie and I were confuse about the precise version of the statements in question.