o-极小理论中的支配单群

IF 0.9 1区数学 Q1 LOGIC

Journal of Mathematical Logic Pub Date : 2020-08-04 DOI:10.1142/S0219061321500306

Rosario Mennuni

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引用次数: 4

摘要

在0极小理论的背景下，研究了整体不变型模控制-等价的单群。我们将其计算简化为证明它是由[公式:见文本]-类型类生成的问题。我们在实闭场中证明了这一点，其中这个单oid的生成器对应于怪物模型的不变凸子。与[C]结合;Ealy, D. Haskell和J. Maríková， real闭值域中的剩余域控制，Notre Dame J. Formal Logic 60(3)(2019) 333-351]，这允许我们计算实闭值域的弱o-极小理论中的控制单oid。

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The domination monoid in o-minimal theories

We study the monoid of global invariant types modulo domination-equivalence in the context of o-minimal theories. We reduce its computation to the problem of proving that it is generated by classes of [Formula: see text]-types. We show this to hold in Real Closed Fields, where generators of this monoid correspond to invariant convex subrings of the monster model. Combined with [C. Ealy, D. Haskell and J. Maríková, Residue field domination in real closed valued fields, Notre Dame J. Formal Logic 60(3) (2019) 333–351], this allows us to compute the domination monoid in the weakly o-minimal theory of Real Closed Valued Fields.

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来源期刊

Journal of Mathematical Logic MATHEMATICS-LOGIC

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Logic (JML) provides an important forum for the communication of original contributions in all areas of mathematical logic and its applications. It aims at publishing papers at the highest level of mathematical creativity and sophistication. JML intends to represent the most important and innovative developments in the subject.