Consistency

In mathematics, a formal system is said to be consistent if none of its proven theorems can also be disproven within that system. Or, alternatively, if the formal system does not assign both true and false as the semantics of one given statement.

To add:

• Systems proved to be consistent
  • Presburger arithmetic
• Systems not proved consistent
• Systems that cannot be proved consistent

See also:

• Gödel's incompleteness theorem