Synonymer & Information om | Engelska ordet AXIOMATIZATION

Exempel på hur man kan använda AXIOMATIZATION i en mening

• Historically, the axiomatization of an ordered field was abstracted gradually from the real numbers, by mathematicians including David Hilbert, Otto Hölder and Hans Hahn.
• The axiom of pairing is generally considered uncontroversial, and it or an equivalent appears in just about any axiomatization of set theory.
• The notion of logical implication for functional dependencies admits a sound and complete finite axiomatization, known as Armstrong's axioms.
• The ordinary axiomatization of second-order arithmetic uses a set-based language in which the set quantifiers can naturally be viewed as quantifying over Cantor space.
• Dilworth (1940) was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts.
• Moreover, an alternative axiomatization of monadic Boolean algebras consists of the (reinterpreted) axioms for an interior algebra, plus ∀(∀x)' = (∀x)' (Halmos 1962: 22).
• Instead, Coxeter gave another proof of the Sylvester–Gallai theorem within ordered geometry, an axiomatization of geometry in terms of betweenness that includes not only Euclidean geometry but several other related geometries.
• Theorem: This axiomatization of deontic logic implies that !x if and only if x is true, OR !x is unsatisfiable.
• Alfred Tarski worked on the axiomatization and metamathematics of Euclidean geometry intermittently from 1926 until his death in 1983, with Tarski (1959) heralding his mature interest in the subject.
• The continuous cycles of deterritorialization and reterritorialization through axiomatization makes up one of the basic rhythms of capitalist society.
• In 1936, Alfred Tarski gave an axiomatization of the real numbers and their arithmetic, consisting of only the eight axioms shown below and a mere four primitive notions: the set of reals denoted R, a binary relation over R, denoted by infix <, a binary operation of addition over R, denoted by infix +, and the constant 1.
• Each of these three properties can be axiomatized with finitely many equations, whence these equations taken together constitute a finite axiomatization of the equational theory of Boolean algebras.
• This allows us to axiomatize the theory using inequalities yet still have a purely equational axiomatization when the inequalities are expanded to equalities.
• in the axiomatization of the two residuals in terms of disjointness, via the equivalence x ≤ y ⇔ x∧¬y = 0.
• This axiomatization is not a class logic in the narrower sense, because in its present form (Zermelo-Fraenkel or NBG) it does not axiomatize the class term, but uses it only in practice as a useful notation.

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