Veblen has given a set of axioms for geometry.!. The first eight of these are as follows : % Axiom I. There exist at least two distinct points. Axiom II. If points A, B, C are in the order ABC, they are in the order CBA. Axiom III. If points A, B, C are in the order ABC, they are not in the order BCA. Axiom IV. If points A, B, C are in the order ABC, then A is distinct from C. Axiom V. If A and...

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 ...

In this article, I draw attention to the value of community in John Mbiti’s philosophy using his famous axiom by reconciling tension between individual and envisages. To do this, offer a reconstruction communitarian axiom: “I am because we are; since are, therefore am.” Mbiti is considered one forerunners debate African philosophy. His axiom, which describes idea Afro-communitarianism, accounts...

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...

One of the major problems of axiom pinpointing for incoherent terminologies is the precise positioning within the conflict axioms. In this paper we present a formal notion for the entailment-based axiom pinpointing of incoherent terminologies, where the parts of an axiom is defined by atomic entailment. Based on these concepts, we prove the one-to-many relationship between existing axiom pinpoi...

The theory of finitary biframes as order-theoretical duals bitopological spaces is explored. category a coreflective subcategory that biframes. Some the advantages adopting pointfree notion bispaces are studied. In particular, it shown for every biframe there which plays role analogue to assembly in frames: L A(L) with universal property analogous frame; and such its main component isomorphic o...

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.