When it comes to synonyms for the phrase "become definite," there are several options to choose from. For instance, you could use the phrase "set in stone" to describe something that's become definite and unchanging. Alternatively, "confirmed" is a stronger synonym that suggests absolute certainty and lack of doubt. "Established" is another option that implies a firm, steady foundation or status. Other synonyms worth considering include "decided," "determined," "settled," and "finalized." Ultimately, the choice of synonym will depend on the context in which the phrase is used and the intended tone or emphasis of the statement.