Decidable theory

Decidable theory refers to a set of mathematical or logical problems where it is possible to determine whether any given statement is true or false using a systematic method or algorithm. In other words, if a theory is decidable, there exists a procedure that can always provide a definitive answer to questions related to that theory. This is in contrast to undecidable theories, where no such procedure exists, meaning some statements can’t be definitively classified as true or false. Decidability is important in fields like computer science, mathematics, and logic as it relates to the limits of what can be computed or proven.