Mechanic Q: Check Engine Light?

My check engine light came on. The first time I took it to the shop they replaced the o2 sensor, the light came back on. The second time they replaced the gas cap, the light came back on. The third time they did a smoke test (I can't recall off hand what they replaced), the light came back on. It's back in again for a forth time. I realize that all the above can throw a check engine light, but everything seems like it can be related in some way. Would the same engine code get thrown each time? If yes, then why not start with the gas cap since it's the cheapest and least labor intensive thing to do? When you check the computer, do you get a list of codes? Or just a single one each time after a reset? I guess when I go back in, I just want some arsenal because this doesn't seem right. Or am I wrong and they're approaching this in the correct order? With the old owner of the shop, I know right now he wouldn't have stood for this. But he sold the shop to his employees. I guess I still felt safe going there, but now I feel like I'm being taken advantage of and I would like to become more informed.

A: Check Engine Light?

Are you saying that a history of the codes are saved?