Republicanism in the United States
The United States Supreme Court has created a basic definition of what a "republic" is.  In United States v. Cruikshank (1875), the court ruled that the "equal rights of citizens" were inherent to the idea of a republic.  Later, the Court's decision from In re Duncan (1891) ruled that the "right of the people to choose their government" is also part of the definition of a republic.