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by Ciro Santilli (@cirosantilli, 37)

Axiom

 Home Mathematics Area of mathematics Formalization of mathematics Formal proof
 1 By others on same topic  0 Discussions  Updated 2025-05-26  +Created 1970-01-01  See my version
  • Table of contents
    • Consistency Axiom
    • Independence (mathematical logic) Axiom

Consistency

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Axiom
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.

Independence (mathematical logic)

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Axiom
A theorem is said to be independent from a set of axioms if it cannot be proven neither true nor false from those axioms.
It or its negation could therefore be arbitrarily added to the set of axioms.

 Ancestors (5)

  1. Formal proof
  2. Formalization of mathematics
  3. Area of mathematics
  4. Mathematics
  5.  Home

 Incoming links (5)

  • CIA 2010 covert communication websites / Reuters article
  • Consistency
  • Euclid's postulates
  • Formalization of mathematics
  • Independence (mathematical logic)

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 Articles by others on the same topic (1)

Axiom by Wikipedia Bot 0  1970-01-01
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