A set of axioms is consistent if they don't lead to any contradictions.
When a set of axioms is not consistent, false can be proven, and then everything is true, making the set of axioms useless.

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Consistency by Wikipedia Bot 0
Consistency can refer to several different concepts depending on the context in which it is used. Here are a few of the most common interpretations: 1. **General Definition**: Consistency refers to the quality of being uniform or coherent over time. It implies stability and reliability in behavior, performance, or characteristics. 2. **In Psychology**: Consistency can relate to a person's behavior and attitudes across different situations.