Can we work through this?

I caught my ex sending messages to two different girls on two different occasions. The first time I told him if he did it again that would be it and took him back. Well he did it again with a completely different girl and I ended things. He’s been begging for me back since I ended things and keeps saying he’s learned his lesson and would never do it again. I told him why would he want to be with me knowing I would never trust him again or at least won’t for a long time and he says he deserves to have to work for it and he will if I take him back. I’m conflicted but a part of me is like you had two chances and still fucked up. Advice?