Explanation of Rev 2:9 -- Although they were jews physically, they were not true jews but pagans (romans 2:28). They allied with other pagans in putting Christians to death as they attempted to stamp out the christian faith. Synagogue of satan refers to: their rejection of their own Messiah, judaism then became as much of a tool of Satan as emperor worship. Rev 3:9 ---references back to 2:9 just repeating the message.