When something is "set in", it means it has become established or fixed. Some synonyms for this phrase include entrenched, ingrained, and deep-rooted. These words imply a sense of something that has been present for a long time and is not easily modified or removed. Other possible synonyms include established, settled, and solidified. Settled implies a sense of agreement or resolution, whereas solidified suggests that something has become firm or secure. In some cases, "set in" can also connote an unpleasant or negative situation, so synonyms for this sense might include hard-wired or inescapable.