In my opinion the ending is mostly an "infinite"loop if elisabeth"infinite" loop. If Elizabeth kills booker thanBooker, then she is not born..cannot exist. so
So who kills bookerBooker,to stop him from becoming comstockComstock? You'll say:well, "Well he's dead..." wellBut if he died theres, there's no one to kill him,so so he dosentdoesn't die, so eliElizabeth gets born and kills him....now you see the loop? Forever turning like bookers skyhookBookers Skyhook....
and bookerAnd Booker from after credits is just,our bookerBooker from a dimentiondimension where baptism never took place the baptism is a variable not a constant the existance of booker is a constant