THE ADDITIVE GROUPS OF AND WITH PREDICATES FOR BEING SQUARE-FREE

Please use this identifier to cite or link to this item: https://doi.org/10.1017/jsl.2020.30

Title:	THE ADDITIVE GROUPS OF AND WITH PREDICATES FOR BEING SQUARE-FREE
Authors:	BHARDWAJ, NEER TRAN, CHIEU-MINH
Issue Date:	Dec-2021
Publisher:	Cambridge University Press (CUP)
Citation:	BHARDWAJ, NEER, TRAN, CHIEU-MINH (2021-12). THE ADDITIVE GROUPS OF AND WITH PREDICATES FOR BEING SQUARE-FREE. The Journal of Symbolic Logic 86 (4) : 1324-1349. ScholarBank@NUS Repository. https://doi.org/10.1017/jsl.2020.30
Abstract:	AbstractWe consider the structures $(\mathbb {Z}; \mathrm {SF}^{\mathbb {Z}})$ , $(\mathbb {Z}; <, \mathrm {SF}^{\mathbb {Z}})$ , $(\mathbb {Q}; \mathrm {SF}^{\mathbb {Q}})$ , and $(\mathbb {Q}; <, \mathrm {SF}^{\mathbb {Q}})$ where $\mathbb {Z}$ is the additive group of integers, $\mathrm {SF}^{\mathbb {Z}}$ is the set of $a \in \mathbb {Z}$ such that $v_{p}(a) < 2$ for every prime p and corresponding p-adic valuation $v_{p}$ , $\mathbb {Q}$ and $\mathrm {SF}^{\mathbb {Q}}$ are defined likewise for rational numbers, and $<$ denotes the natural ordering on each of these domains. We prove that the second structure is model-theoretically wild while the other three structures are model-theoretically tame. Moreover, all these results can be seen as examples where number-theoretic randomness yields model-theoretic consequences.
Source Title:	The Journal of Symbolic Logic
URI:	https://scholarbank.nus.edu.sg/handle/10635/242965
ISSN:	0022-4812 1943-5886
DOI:	10.1017/jsl.2020.30
Appears in Collections:	Staff Publications Elements

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