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A criterion for uniform finiteness in the imaginary sorts
- Source :
- Archive for Mathematical Logic. 61:583-589
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- Let $T$ be a theory. If $T$ eliminates $\exists^\infty$, it need not follow that $T^{eq}$ eliminates $\exists^\infty$, as shown by the example of the $p$-adics. We give a criterion to determine whether $T^{eq}$ eliminates $\exists^\infty$. Specifically, we show that $T^{eq}$ eliminates $\exists^\infty$ if and only if $\exists^\infty$ is eliminated on all interpretable sets of "unary imaginaries." This criterion can be applied in cases where a full description of $T^{eq}$ is unknown. As an application, we show that $T^{eq}$ eliminates $\exists^\infty$ when $T$ is a C-minimal expansion of ACVF.<br />Comment: 6 pages
Details
- ISSN :
- 14320665 and 09335846
- Volume :
- 61
- Database :
- OpenAIRE
- Journal :
- Archive for Mathematical Logic
- Accession number :
- edsair.doi.dedup.....dda4e5862c6b6a92444708d9e0d58abf