"Admitted fact" refers to a truth or reality that is widely accepted and acknowledged. There are several synonyms for this term that can be used interchangeably in different contexts. For instance, "established fact" is a commonly used synonym that implies the fact being firmly established and accepted in a particular field or society. "Undisputed truth" suggests that the fact is well-known and not subject to dispute or question. "Certified truth" conveys the idea that the fact has been verified and validated by a relevant authority or expert. Other synonyms for "admitted fact" include "acknowledged reality," "accepted verity," and "recognized certainty." Choosing the right synonym depends on the context and intended tone of your writing or speech.