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NOUN | an axiom | axioms | |

SYNO | axiom | maxim |

mat. aksiomë {f} | axiom |

Usage Examples English

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- ACA0 is defined as the theory consisting of the basic axioms, the arithmetical comprehension
**axiom**scheme (in other words the comprehension axiom for every "arithmetical" formula "φ") and the ordinary second-order induction axiom. - Luce's choice
**axiom**1 is implied by choice axiom 2. - In mathematical logic, an
**axiom**schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom. - Thus, the wholeness
**axiom**differs from Reinhardt cardinals (another way of providing elementary embeddings from "V" to itself) by allowing the axiom of choice and instead modifying the axiom of replacement. - Since "S" is his 1929
**axiom**system, von Neumann's 1925 axiom system is consistent relative to his 1929 axiom system, which is closer to Cantorian set theory.

- By the 7th edition of the "Grundlagen", this
**axiom**had been replaced by the axiom of line completeness given above and the old axiom V.2 became Theorem 32. - The subcountibility
**axiom**, asserting all sets are subcountable, is incompatible with any new axiom making [...] countable, including LEM. - Under this definition, we can modify "homotopy
**axiom**" for cohomology to a "proper homotopy axiom" if we define a coboundary homomorphism [...] only when [...] is a "closed" subset. - Proving that the
**axiom**of separation, axiom of replacement, and axiom of choice hold in [...] requires (at least as shown above) the use of a reflection principle for [...].

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