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| 1 | List of axioms |
| This is a list of axioms as that term is understood in mathematics, by Wikipedia page. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system. Zermelo-Frankel axioms These are the de facto ... | |
| 2 | Arthur Wightman |
| Arthur Strong Wightman is an American mathematical physicist. He is one of the founders of quantum field theory, and originated the set of Wightman axioms. See also: Streater-Wightman axioms Garding-Wightman axioms ... | |
| 3 | Axiom schema |
| finite number of axioms. For this reason, an axiom schema is used. Formally, an axiom schema is a set (usually infinite) of well formed formulae, each of which is taken to be an axiom. Often, this set is constructed recursively. A well known axiom schema is the axiom schema of replacement. There is ... | |
| 4 | Axiom of countable choice |
| The axiom of countable choice or axiom of denumerable choice is an axiom of set theory similar to the axiom of choice. It states that a countable collection of sets must have a choice function. Paul Cohen showed that this is not provable in ZF. This axiom is required for the development of analysis ... | |
| 5 | Axiom (algebra software) |
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| 6 | Axiom computer algebra system |
| Axiom is a computer algebra system originally developed by researchers at IBM under the name Scratchpad ... | |
| 7 | Axiom of empty set |
| , the axiom of empty set is one of the axioms of Zermelo-Fraenkel set theory. In the formal language of the Zermelo-Frankel axioms, the axiom reads: ∃ A , ∀ B , ¬( B ∈ A ); or in words: There is a set A such that, given any set B , B is not a member of A . We can use the axiom of ... | |
| 8 | Axiomatic |
| In mathematics, an axiomatic theory is one based on axioms. Axiomatic is a collection of short stories by Greg Egan ... | |
| 9 | Löb's theorem |
| In mathematical logic, Löb's theorem states that if a set of axioms proves the Peano axioms, the... provable. Theorem First, Let Prov T(φ) mean that there exists a proof of φ in T If a set of axioms T is such that where PA are the Peano axioms of arithmetic, then for all sentences φ , if and only if ... | |
| 10 | Axiom schema of specification |
| , the axiom schema of specification , or axiom schema of separation , or axiom schema of restricted comprehension , is a schema of axioms in Zermelo-Fraenkel set theory. It is also called the axiom... language of the Zermelo-Fraenkel axioms, the axiom schema reads: or in words: Given any set A ... | |
| 11 | Axiom of dependent choice |
| In mathematics, the axiom of dependent choice is a weak form of the axiom of choice which is still sufficient to develop most of real analysis. The axiom can be stated as follows: For any nonempty... X such that aRb .) Note that even without such an axiom we could form the first n terms of such a ... | |
| 12 | Axiom of pairing |
| , the axiom of pairing is one of the axioms of Zermelo-Fraenkel set theory. In the formal language of the Zermelo-Frankel axioms, the axiom reads: ∀ A , ∀ B , ∃ C , ∀ D , D ∈ C ↔ ( D = A â... , D is a member of C if and only if D is equal to A or D is equal to B . What the axiom is really ... | |
| 13 | Axiom of power set |
| In mathematics, the axiom of power set is one of the Zermelo-Fraenkel axioms of axiomatic set theory. In the formal language of the Zermelo-Fraenkel axioms, the axiom reads: ∀ A , ∃ B , ∀ C... , then D is a member of A . To understand this axiom, note that the clause in parentheses in the ... | |
| 14 | Axiom of union |
| , the axiom of union is one of the axioms of Zermelo-Fraenkel set theory, stating that, for any two...-Fraenkel axioms, the axiom reads: ∀ A , ∃ B , ∀ C , C ∈ B ↔ (∃ D , D ∈ A ∧ C ∈ D... understand this axiom, note that the clause involving D in the symbolic statement above states that C is a ... | |
| 15 | Jules Richard |
| Jules Antoine Richard (1862-1956) was a French mathematician. He authored Sur la nature des axiomes de la géométrie , an investigation of the nature of axioms in geometry: are they necessarily true, are they arbitrary assumptions, are they definitions? He is best remembered for creation of the ... |