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1.
We show that if G is a definably compact, definably connected definable group defined in an arbitrary o‐minimal structure, then G is divisible. Furthermore, if G is defined in an o‐minimal expansion of a field, k ∈ ? and pk : GG is the definable map given by pk (x ) = xk for all xG , then we have |(pk )–1(x )| ≥ kr for all xG , where r > 0 is the maximal dimension of abelian definable subgroups of G . (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   
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模型论简介     
本文将模型论介绍为“可定义集的数学”.首先给出“可定义集”的确切定义,并引入处理可定义集的主要工具——一阶公式的概念.然后给出一些例子.最后介绍一些相当于可定义集的组合性质的稳定性理论.  相似文献   
4.
We prove that every type of finite Cantor‐Bendixson rank over a model of a first‐order theory without the strict order property is definable and has a unique nonforking extension to a global type. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim  相似文献   
5.
We study the first-order definable, Diophantine, and algebraic subsets in the set of all ordered sets generating a group or generating a group as a normal subgroup for some relatively free solvable groups.  相似文献   
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We define and investigate a uniformly locally o-minimal structure of the second kind in this paper. All uniformly locally o-minimal structures of the second kind have local monotonicity, which is a local version of monotonicity theorem of o-minimal structures. We also demonstrate a local definable cell decomposition theorem for definably complete uniformly locally o-minimal structures of the second kind. We define dimension of a definable set and investigate its basic properties when the given structure is a locally o-minimal structure which admits local definable cell decomposition.  相似文献   
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A proof is given that 0 ′ (the argest Turing degree containing a computably enumerable set) is definable in the structure of the degrees of unsolvability. This answers a long‐standing question of Kleene and Post, and has a number of corollaries including the definability of the jump operator.  相似文献   
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Given a locally presentable additive category A, we study a class of covariantly finite subcategories which we call definable. A definable subcategory arises from a set of coherent functors F i on A by taking all objects X in A such that F i X=0 for all i. We give various characterizations of definable subcategories, demonstrating that all covariantly finite subcategories which arise in practice are of this form. This is based on a filtration of the category of all coherent functors on A.  相似文献   
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We prove three theorems extending Sard's theorem and its infinite dimensional extension due to Smale to set-valued mappings with stratifiable graphs. The very concept of a critical value comes from (nonsmooth) variational analysis and turns out to be perfectly compatible with the natural condition defining ``good' stratifications (e.g., Whitney stratification in the finite dimensional case).

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10.
Herrmann  Christian 《Order》2000,17(4):387-390
The sizes of Boolean combinations of subgroups G i of a finite abelian group depends only on the Boolean expression, the 0-1-sublattice generated by the G i , and the size of minimal subquotients from this sublattice. Moreover, they increase, monotonically, with those sizes.  相似文献   
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