The phrase "without appeal" is often used to describe a final decision or judgment that cannot be challenged or questioned further. There are several synonyms that can be used in place of this phrase, depending on the context and tone of the sentence. Some of these synonyms include "irrevocable," "unanimous," "conclusive," "decisive," "final," "unchallenged," and "definite." These words can convey a sense of certainty and finality, indicating that there is no room for debate or disagreement. Although the exact synonym used may vary, all of these words convey a similar sense of an outcome that cannot be changed or disputed.