通过约简进行泛型展开

IF 0.9 1区数学 Q1 LOGIC

Journal of Mathematical Logic Pub Date : 2018-10-27 DOI:10.1142/S0219061321500161

Christian d'Elb'ee

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引用次数: 15

摘要

考虑用一个谓词对[公式:见文本]的约化[公式:见文本]的子模型展开[公式:见文本]的理论[公式:见文本]。我们提出了一种设置，在这种设置中，这个展开式允许有一个模型伴随物[公式:见正文]。我们展示了理论[公式:见文]的一些好的特征转移到[公式:见文]。特别地，我们研究了这种展开式保持[公式:见文]的稳定性，即起始理论[公式:见文]的简单性或稳定性的条件。我们给出了通过这一过程得到的新的[公式:见文]不简单理论的具体例子，其中有一个完美的[公式:见文]无正特征的PAC域用一般加性子群展开，以及一个任意特征的代数闭域用一般乘性子群展开。

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Generic expansions by a reduct

Consider the expansion [Formula: see text] of a theory [Formula: see text] by a predicate for a submodel of a reduct [Formula: see text] of [Formula: see text]. We present a setup in which this expansion admits a model companion [Formula: see text]. We show that some of the nice features of the theory [Formula: see text] transfer to [Formula: see text]. In particular, we study conditions for which this expansion preserves the [Formula: see text]-ness, the simplicity or the stability of the starting theory [Formula: see text]. We give concrete examples of new [Formula: see text] not simple theories obtained by this process, among them the expansion of a perfect [Formula: see text]-free PAC field of positive characteristic by generic additive subgroups, and the expansion of an algebraically closed field of any characteristic by a generic multiplicative subgroup.

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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.