Consistency (original) (raw)

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Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology

Alphabetical Index New in MathWorld

• Foundations of Mathematics
• Logic
• General Logic

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.

See also

Axiomatic Set Theory, Axiomatic System, Complete Axiomatic Theory, Consistency Strength,Gödel's First Incompleteness Theorem, Gödel's Second Incompleteness Theorem

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Cite this as:

Weisstein, Eric W. "Consistency." FromMathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Consistency.html

Subject classifications

• Foundations of Mathematics
• Logic
• General Logic