自同构与强不变关系

IF 0.6 4区 数学 Q3 MATHEMATICS
Ferdinand Börner, Martin Goldstern, Saharon Shelah
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引用次数: 0

摘要

我们研究了基集a上的有限关系集与其自同构之间的Galois连接({{,\textrm{Aut}\,}}\)-\({},\text rm{sInv}\,})的特征。特别地,对于\(A=\omega_1\),我们构造了一个关系的可数集R,它在关系上的所有不变运算和任意交集下是闭的,但在\({\textrm{sInv-Aut}})下不是闭的。我们的结构(A,R)具有\(\omega\)-范畴一阶理论。高阶可定义的阱阶使其具有刚性,但对有限语言的任何简化都是同构的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Automorphisms and strongly invariant relations

Automorphisms and strongly invariant relations

We investigate characterizations of the Galois connection \({{\,\textrm{Aut}\,}}\)-\({{\,\textrm{sInv}\,}}\) between sets of finitary relations on a base set A and their automorphisms. In particular, for \(A=\omega _1\), we construct a countable set R of relations that is closed under all invariant operations on relations and under arbitrary intersections, but is not closed under \({\textrm{sInv Aut}}\). Our structure (AR) has an \(\omega \)-categorical first order theory. A higher order definable well-order makes it rigid, but any reduct to a finite language is homogeneous.

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来源期刊
Algebra Universalis
Algebra Universalis 数学-数学
CiteScore
1.00
自引率
16.70%
发文量
34
审稿时长
3 months
期刊介绍: Algebra Universalis publishes papers in universal algebra, lattice theory, and related fields. In a pragmatic way, one could define the areas of interest of the journal as the union of the areas of interest of the members of the Editorial Board. In addition to research papers, we are also interested in publishing high quality survey articles.
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