A. Negotiate the decision. Be open to the possibility but realize you can't go back to what you had. If he wants to come home and figure out how to have a truly committed, loving relationship that includes forgiveness, repentance, the miracle of God's healing and living a reconciled life that demonstrates God's powerful grace, this could be a good thing. If he is just tired of living accidentally it is unlikely things have changed.
Q. There was lots of betrayal, lies and other women, so what should my first requirement be?
A. The first question I believe is "What has changed?" If you like the answer, I think the next question is, "How can I know I am the only woman in your life?" The burden is on him to convince you of this through transparency and accountability. If you notice signs of real change then you want to ask God to give you His grace to forgive and reconnect since it will be a miracle.
Q. What kind of evidence, in husband, will point to that?
A. It is hard to say because he really needs to convince you. It will include words you are not used to hearing from him, body language that makes him believable, a look in his eyes that is different than what you have seen in the past, and a realistic accountability system he sets up with men to help him grow.