axiomatize การใช้

• Grothendieck topologies axiomatize the notion of an open cover.
• The Peano Axioms ( described below ) thus only partially axiomatize this theory.
• This result shows that it is possible to axiomatize ZFC with a single infinite axiom schema.
• We first axiomatize NBG using the.
• Weierstrass began to advocate the arithmetization of analysis, to axiomatize analysis using properties of the natural numbers.
• This allows us to axiomatize the theory using inequalities yet still have a purely equational axiomatization when the inequalities are expanded to equalities.
• Andr?Weil's Weil conjectures stated that there was a Grothendieck topologies, which axiomatize the notion of " covering ".
• There have been several attempts to axiomatize the underlying rings of von Neumann algebras, including Baer *-rings and AW * algebras.
• Zermelo began to axiomatize set theory in 1905; in 1908, he published his results despite his failure to prove the consistency of his axiomatic system.
• We axiomatize predicate calculus " without equality ", i . e . there are no special axioms expressing the properties of equality as a special relation symbol.
• Although modal logic is not often used to axiomatize mathematics, it has been used to study the properties of first-order provability ( Hamkins and L鰓e 2007 ).
• When scientists attempt to formalize the principles of the empirical sciences, they use an interpretation to model reality, in the same way logicians axiomatize the principles of logic.
• In the early 20th century, David Hilbert led a program to axiomatize all of mathematics with precise axioms and precise logical rules of deduction which could be performed by a machine.
• But anybody who has seriously tried to axiomatize that elusive concept, will probably concur with it . "  " VNM 1953 ?3.7 . 1, p . 28 ".
• Not a class logic in the narrower sense, but in its present form ( ZF or NBG ) because it does not axiomatize the class term, but used only in practice as a useful notation.
• However, it is possible to axiomatize the above procedure and give conditions under which the above spectral sequence holds for a general ( co ) homology theory, see Smith's original work or the introduction in.
• The axiom schemata of replacement and separation each contain infinitely many instances . included a result first proved in his 1957 Ph . D . thesis : if ZFC is consistent, it is impossible to axiomatize ZFC using only finitely many axioms.
• This THIRD INSIGHT is referring to Hilbert's second problem and Hilbert's ongoing attempt to axiomatize all of arithmetic, and with this system, to discover a " consistency proof " for all of mathematics  see more below.
• Attempts to axiomatize the empirical sciences, Carnap said, use a " descriptive interpretation " to model reality . :-the world is an interpretation ( or model ) of these sciences, only insofar as these sciences are true.
• Students who in turn learned logic at Royce's feet include Clarence Irving Lewis, who went on to pioneer modal logic, Edward Vermilye Huntington, the first to axiomatize Boolean algebra, and Henry M . Sheffer, known for his eponymous stroke.