Une théorie générale des infinitésimaux
Un'estensione del teorema di Löb
Unification for nilpotent groups of class 2.
Unification in varieties of idempotent semigroups.
Unification of higher-order patterns modulo simple syntactic equational theories.
Uniform p-adic cell decomposition and local zeta functions.
Uniform reducibility of representability problems for algebraic structures.
Uniform Space
In this article, we formalize in Mizar [1] the notion of uniform space introduced by André Weil using the concepts of entourages [2]. We present some results between uniform space and pseudo metric space. We introduce the concepts of left-uniformity and right-uniformity of a topological group. Next, we define the concept of the partition topology. Following the Vlach’s works [11, 10], we define the semi-uniform space induced by a tolerance and the uniform space induced by an equivalence relation....
Uniformization and anti-uniformization properties of ladder systems
Natural weakenings of uniformizability of a ladder system on ω₁ are considered. It is shown that even assuming CH all the properties may be distinct in a strong sense. In addition, these properties are studied in conjunction with other properties inconsistent with full uniformizability, which we call anti-uniformization properties. The most important conjunction considered is the uniformization property we call countable metacompactness and the anti-uniformization property we call thinness. The...
Uniformization of rigid subanalytic sets
Uniformly completely Ramsey sets
Galvin and Prikry defined completely Ramsey sets and showed that the class of completely Ramsey sets forms a σ-algebra containing open sets. However, they used two definitions of completely Ramsey. We show that they are not equivalent as they remarked. One of these definitions is a more uniform property than the other. We call it the uniformly completely Ramsey property. We show that some of the results of Ellentuck, Silver, Brown and Aniszczyk concerning completely Ramsey sets also hold for uniformly...
Unimodular rows over Laurent polynomial rings
We prove that for any ring of Krull dimension not greater than 1 and , the group acts transitively on . In particular, we obtain that for any ring with Krull dimension not greater than 1, all finitely generated stably free modules over are free. All the obtained results are proved constructively.
Unions and Intersections of Isomoryhic Images of Nonstandard Models of Arithmetic
Unions of subquasigroups
Unique irredundant decompositions in upper continuous lattices
Uniqueness of bounded observables
Uniqueness of means in the Cohen model
We investigate the question of whether or not an amenable subgroup of the permutation group on can have a unique invariant mean on its action. We extend the work of M. Foreman (1994) and show that in the Cohen model such an amenable group with a unique invariant mean must fail to have slow growth rate and a certain weakened solvability condition.
Universal analytic preorders arising from surjective functions
Examples are presented of Σ₁¹-universal preorders arising by requiring the existence of particular surjective functions. These are: the relation of epimorphism between countable graphs; the relation of being a continuous image (or a continuous image of some specific kind) for continua; the relation of being continuous open image for dendrites.
Universal cyclic relations
Universal functions
A function of two variables F(x,y) is universal if for every function G(x,y) there exist functions h(x) and k(y) such that G(x,y) = F(h(x),k(y)) for all x,y. Sierpiński showed that assuming the Continuum Hypothesis there exists a Borel function F(x,y) which is universal. Assuming Martin's Axiom there is a universal function of Baire class 2. A universal function cannot be of Baire class 1. Here we show that it is consistent that for each α with 2 ≤ α < ω₁ there...