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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.
© dict.cc Dutch-English dictionary 2023
Contains translations by TU Chemnitz and Mr Honey's Business Dictionary (German-English only).
Links to this dictionary or to individual translations are very welcome!