Th (N，·)$ \operatorname{Th}(\mathbb {N}，\cdot)$

IF 0.4 4区数学 Q4 LOGIC

Mathematical Logic Quarterly Pub Date : 2022-04-28 DOI:10.1002/malq.202100049

Atticus Stonestrom

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引用次数: 1

摘要

“Skolem算术”是乘法单群(N，·)$ (\mathbb {N}，\cdot)$的完备理论T。给出了T的 \ \var \ \可定义稳定嵌入集的完整刻划，特别证明了在具有相同可定义闭包的关系之前，只有一个非平凡的闭包:无平方元的集合。然后我们证明了T有弱消虚数，但没有消有限虚数。

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Some model theory of Th ( N , · ) $\operatorname{Th}(\mathbb {N},\cdot )$

‘Skolem arithmetic’ is the complete theory T of the multiplicative monoid $(N, \cdot)$ . We give a full characterization of the $⌀$ -definable stably embedded sets of T, showing in particular that, up to the relation of having the same definable closure, there is only one non-trivial one: the set of squarefree elements. We then prove that T has weak elimination of imaginaries but not elimination of finite imaginaries.

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来源期刊

Mathematical Logic Quarterly 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematical Logic Quarterly publishes original contributions on mathematical logic and foundations of mathematics and related areas, such as general logic, model theory, recursion theory, set theory, proof theory and constructive mathematics, algebraic logic, nonstandard models, and logical aspects of theoretical computer science.