Its axiomatization allows for non-additive probabilities and the expected utility of an act is defined using a Choquet integral.
32.
Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry.
33.
However, they will always prove some theorems as both true and false, for an axiomatization not simpler than Peano arithmetic.
34.
Lejewski then goes on to extend this interpretation to the language of inclusion, and presents an axiomatization of an unrestricted logic.
35.
There are several properties that a formal system may have, including completeness, consistency, and the existence of an effective axiomatization.
36.
This allows us to axiomatize the theory using inequalities yet still have a purely equational axiomatization when the inequalities are expanded to equalities.
37.
Redko showed in 1967 that these equations had no finite axiomatization, for which John Horton Conway gave a shorter proof in 1971.
38.
In addition to removing ambiguity from previously naive terms such as function, it was hoped that this axiomatization would allow for consistency proofs.
39.
A well-known axiomatization, comprising three axiom schemata and one inference rule ( " modus ponens " ), is:
40.
He also objected strongly to the philosophical implications of countable models of set theory, which followed from Skolem's first-order axiomatization.
