The phrase "not for anything in the world" is used to indicate something that is absolutely impossible or undesirable and cannot be changed under any circumstances. Some synonyms for this expression are "under no circumstances", "never in a million years", "not in a thousand years", "not for love or money", "not in this lifetime", "no way in hell", "not in a million lifetimes", "absolutely not", "not at any cost", "not on your life", and "not even if you paid me". These phrases express a firm determination or refusal to do something, and convey a sense of finality or decisive rejection.