A non-trivial, transitive and reflexive binary relation on the set of lotteries satisfying independence that also satisfies any two of the following three axioms satisfies the third: completeness, Archimedean and mixture continuity (Dubra (2011)). This paper generalizes Dubra’s result in two ways: First, by replacing independence with a weaker betweenness axiom. Second, by replacing independenc...

A recently proposed axiom system for André’s central translation structures is improved upon. First, one of its axioms turns out to be dependent (derivable from the other axioms). Without this axiom, the axiom system is indeed independent. Second, whereas most of the original independence models were infinite, finite independence models are available. Moreover, the independence proof for one of...

1 The Axioms of Quantum Mechanics 1 1.1 The State Space Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Unitary Evolution Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 The Measurement Axiom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.4 The Composite System Axiom . . . . . . . . . . . . . . . . . . ...

The Maschler–Owen consistent value for non-transferable utility games is axiomatized, by means of a marginality axiom. JEL Classification: C7, D7

Let f be a diffeomorphism of a closed C∞ manifold M . In this paper, we introduce the notion of the C1-stable specification property for a closed f -invariant set Λ of M , and we prove that f|Λ satisfies a C 1-stable specification property if and only if Λ is a hyperbolic elementary set. As a corollary, the C1-interior of the set of diffeomorphisms of M satisfying the specification property is ...

We show there is a residual set of non-Anosov C∞ Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. If M is a surface and 2 ≤ r ≤ ∞, then we will show there exists an open and dense set of of Cr Axiom A diffeomorphisms with the no cycles property whose elements have trivial centralizer. Additionally, we examine commuting diffeomorphisms preserving a com...

Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.

Rough set axiomatization is one aspect of rough set study to characterize rough set theory using dependable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. The classic rough set theory is based on equivalent relation, but rough set theory based on reflexive and transitive relation (called quasi-ordering) has wide applications in the real world....

The beginnings of set theory date back to the late nineteenth century, to the work of Cantor on aggregates and trigonometric series, which culminated into his seminal work Contributions to the Founding of the Theory of Transfinite Numbers [2]. Although this work was published in 1895 and 1897, in two parts, the theory of sets had been established as an independent branch of mathematics as early...

Jan von Plato proposed in 1998 an intuitionist axiomatization of ordered affine geometry consisting 22 axioms. It is shown that axiom I.7, which equivalent to a conjunction four statements, two are redundant, can be replaced with simpler axiom, Plato’s Theorem 3.10.