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Preprint Number 1715

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1715. Will Johnson
A criterion for uniform finiteness in the imaginary sorts

Submission date: 6 January 2020


Let T be a theory. If T eliminates \exists^\infty, it need not follow that T^{eq} eliminates ∃^∞, as shown by the example of the p-adics. We give a criterion to determine whether T^{eq} eliminates ∃^∞. Specifically, we show that T^{eq} eliminates ∃^∞ if and only if ∃^∞ 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 ∃^∞ when T is a C-minimal expansion of ACVF.

Mathematics Subject Classification: 03C07, 03C68 \\

Keywords and phrases:

Full text arXiv 2001.01528: pdf, ps.

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