Sentence examples for weak axiom from inspiring English sources

To avoid this undesirable conclusion, only those choices are considered that satisfy the Weak Axiom of Revealed Preferences (WARP).

This is a survey of the systematic study of weak axiom systems for Arithmetic (in short: "Weak Arithmetics"), which plays a growing and unifying role in various kinds of investigations:.

Indeed, a few mathematicians have developed probability theory with only the weaker axiom of finite additivity, but the absence of interesting models that fail to satisfy the axiom of countable additivity has led to its virtually universal acceptance.

The authors of[24] attempted to replace individual rationality in Hurwicz's result with a weaker axiom of non-dictatorship.

The Collection axiom is replaced by two weaker axioms.

They satisfy the weakest axioms, the weakest constraints on the logic of uncertainty.

If ∀A(T[¬A] ↔ ¬TA) is retained, one will have to find weaker axioms or rules for truth iteration, but truth remains a classical concept in the sense that ∀A(T[¬A] ↔ ¬TA) implies the law of excluded middle (for any sentence either the sentence itself or its negation is true) and the law of noncontradiction (for no sentence the sentence itself and its negation are true).

Although until now there has never been given a completely satisfactory justification of most continuity axioms for arbitrary choice sequences, not even by Brouwer, when restricted to the class of lawless sequences arguments supporting the validity of the weak continuity axiom run as follows.

The weak continuity axiom has been shown to be consistent, and is often applied in a form that can be justified, namely in the case in which the predicate $A$ only refers to the values of $\alpha$, and not to the higher order properties that it possibly possesses.

Suppose that η satisfies the weak discrete reliability axiom  (B4).

Lemma 8.9 Suppose that η satisfies the weak discrete reliability axiom  (B4).