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NOUN | an axiom | axioms |

wisk. axioma's {mv} | axioms |

Usage Examples English

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- Today's student of geometry has
**axioms**other than Euclid's available: see Hilbert's axioms and Tarski's axioms. - Formal ethics has four
**axioms**in addition to the axioms of predicate and modal logic. - Forcing
**axioms**are viable candidates for extending the axioms of set theory as an alternative to large cardinal axioms. - From these
**axioms**, Huntington derived the usual axioms of Boolean algebra. - On the other hand, David Hilbert proposed a set of
**axioms**, inspired by Euclid's postulates. - The first four groups of
**axioms**of Hilbert's axioms for plane geometry are bi-interpretable with Tarski's axioms minus continuity. - Each of Frege's
**axioms**can be derived from the standard axioms, and each of the standard axioms can be derived from Frege's axioms. - This section gives examples of mathematical theories that are developed entirely from a set of non-logical
**axioms**(axioms, henceforth). - The
**axioms**of pairing and regularity, which were needed for the proof of the class existence theorem, have been given above. - In mathematical logic, the Peano
**axioms**(or Peano postulates or Dedekind–Peano axioms), are axioms for the natural numbers presented in the 19th century by the German mathematician Richard Dedekind and by the Italian mathematician Giuseppe Peano. - In 1964 van Zwet proposed a series of
**axioms**for ordering measures of skewness. The nonparametric skew does not satisfy these axioms. - The deductive systems considered by Shapiro (1991) and Henkin (1950) add to the augmented first-order deductive scheme both comprehension
**axioms**and choice axioms. - Starting with Hilbert's
**axioms**the necessary changes involve removing Hilbert's four axioms of order and replacing them with these seven axioms of separation concerned with a new undefined relation. - An algebraic structure is a set equipped with operations that satisfy some
**axioms**.

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