Locally Polynomially Bounded Structures

多项式有界o-极小结构中可积轨迹的可定义性

Definability of the Integrability Locus in Polynomially Bounded o-Minimal Structures

本文整合现有文献论证，证明在实数域的任何o-极小扩张中，可定义集族对应有限体积纤维的参数集是可定义的。

The elementary theory of Dedekind cuts in polynomially bounded structures

Let M be a polynomially bounded, o-minimal structure with archimedean prime model, for example if M is a real closed field. Let C be a convex and unbounded subset of M. We determine the first order theory of the structure M expanded by the set C. We do this also over any given set of parameters from M, which yields a description of all subsets of M^n, definable in the expanded structure.

Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation

This article presents two constructions motivated by a conjecture of L. van den Dries and C. Miller concerning the restricted analytic field with exponentiation. The first construction provides an example of two o-minimal expansions of a real closed field that possess the same field of germs at infinity of one-variable functions and yet define different global one-variable functions. The second construction gives an example of a family of infinitely many distinct polynomially bounded reducts (all this in the sense of definability) of the restricted analytic field with exponentiation.

对数解析函数的增长

Growth of Log-Analytic Functions

本文研究对数解析函数的增长性，证明一元函数是多项式有界的，指出高维全局情形可能呈指数增长，并证明其在包含无穷远射线芽的可定义集上多项式有界。

多项式有界o-最小曲线在齐性空间中的等分布

Equidistribution of polynomially bounded o-minimal curves in homogeneous spaces

研究多项式有界o-最小曲线在齐性空间中的等分布性质，证明非收缩曲线轨迹的等分布定理及相关测度的不变性。

Locally Roelcke precompact Polish groups

A Polish group is said to be locally Roelcke precompact if there is a neighborhood of the identity element that is totally bounded in the Roelcke (or lower) group uniformity. These form a subclass of the locally bounded groups, while generalizing the Roelcke precompact and locally compact Polish groups. We characterize these groups in terms of their geometric structure as those locally bounded groups whose coarsely bounded sets are all Roelcke precompact, and in terms of their uniform structure as those groups whose completions in the Roelcke uniformity are locally compact. We also assess the …