Translation for 'axiomatisation' from English to Portuguese

axiomatisation [Br.]

axiomatização {f}

• With a second rule of uniform substitution (US), we can change each of these axiom schemes into a single axiom, replacing each schematic variable by some propositional variable that isn't mentioned in any axiom to get what we call the substitutional axiomatisation.
• The axiom of extensionality is generally uncontroversial in set-theoretical foundations of mathematics, and it or an equivalent appears in just about any alternative axiomatisation of set theory.
• The downward form of this theorem shows that if a countable first-order axiomatisation is satisfied by any infinite structure, then the same axioms are satisfied by some countable structure.
• It is also an important step in the Heunen-Kornell axiomatisation of the category of Hilbert spaces.
• It was taken as an axiom in his first axiomatisation of propositional logic.

• For theories such as second-order arithmetic, the existence of non-standard interpretations of higher-order domains isn't just a deficiency of the particular axiomatisation derived from type theory that Henkin used, but a necessary consequence of Gödel's incompleteness theorem: Henkin's axioms can't be supplemented further to ensure the standard interpretation is the only possible model.