A criterion for uniform finiteness in the imaginary sorts

Autor: Will Johnson
Rok vydání: 2021
Předmět:
Zdroj: Archive for Mathematical Logic. 61:583-589
ISSN: 1432-0665
0933-5846
DOI: 10.1007/s00153-021-00803-5
Popis: 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.
Comment: 6 pages
Databáze: OpenAIRE
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