有序转幂域

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-12-02 DOI:10.1016/j.apal.2024.103541

Lothar Sebastian Krapp , Salma Kuhlmann

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引用次数: 0

摘要

我们在{+，⋅,0,1,<,e，T}语言中建立了有序转幂域的一阶理论，其中e和T代表一元函数符号。虽然该理论的阿基米德模型很容易描述，但对非阿基米德模型的研究导致了对剩余场和自然估值下的值群的诱导结构的系统检查。在有序指数域（K,e）的值群上建立了允许转幂函数T与e相容的充要条件，并给出了所有可数有序转幂域的赋值理论不变量的完整刻画。

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Ordered transexponential fields

We develop a first-order theory of ordered transexponential fields in the language

{+, \cdot, 0, 1, <, e, T}

, where e and T stand for unary function symbols. While the archimedean models of this theory are readily described, the study of the non-archimedean models leads to a systematic examination of the induced structure on the residue field and the value group under the natural valuation. We establish necessary and sufficient conditions on the value group of an ordered exponential field

(K, e)

to admit a transexponential function T compatible with e. Moreover, we give a full characterisation of all countable ordered transexponential fields in terms of their valuation theoretic invariants.

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.