1 Three Axioms for a Determinant Function Let d be a scalar-valued function on the space Mn×n of all n×n matrices. Let A1, A2, . . . , An be the n rows of an n×n matrix A. We will denote the value d(A) of A under the function d as d(A) = d(A1, A2, . . . , An), indicating that d is a scalar-valued function of n n-dimensional row vectors A1, A2, . . . , An. The scalar-valued function d is called ...

If the Wholeness Axiom WA0 is itself consistent, then it is consistent with v=hod. A consequence of the proof is that the various Wholeness Axioms are not all equivalent. Additionally, the theory zfc+wa0 is finitely axiomatizable. The Wholeness Axioms, proposed by Paul Corazza, occupy a high place in the upper stratosphere of the large cardinal hierarchy. They are intended as weakenings of the ...

We introduce the Bounded Axiom A Forcing Axiom(BAAFA). It turns out that it is equiconsistent with the existence of a regular Σ2-correct cardinal and hence also equiconsistent with BPFA. Furthermore we show that, if consistent, it does not imply the Bounded Proper Forcing Axiom(BPFA).

We introduce a new abstract approach to the study of conditional independence, founded on a concept analogous to the factoriza-tion properties of probabilistic independence, rather than the separation properties of a graph. The basic ingredient is the \con-ditional product", which provides a way of combining the objects under consideration while preserving as much independence as possible. We i...

We prove that a random choice rule satisfies Luce's Choice Axiom if and only its support is correspondence the Weak of Revealed Preference, thus it consists alternatives are optimal according to some preference, then occurs tie-breaking mechanism among such Renyi's Conditioning Axiom. Our result shows is, in precise formal sense, probabilistic version It supports view his own axiom as “canon ra...

The usual way to study the local structure of Equilibrium State of an Axiom-A diffeomorphism or flow is to use the symbolic dynamic and to push results on the manifold. A new geometrical method is given. It consists in proving that Equilibrium States for Hölder-continuous functions are related to other Equilibrium States of some special sub-systems satisfying a sort of expansiveness. Using diff...