Submission date:

Abstract:

Outside of the framework of geometric theories, we exhibit complete, respectively model-complete theories of rings whose corresponding theory of pairs is complete, respectively model-complete, using transfer results proven in the seventies for boolean products of structures. It includes certain boolean products of pairs of dp-minimal fields of characteristic 0. We also show, as in the case of pairs of fields, how it fits in the framework of differential rings.

Mathematics Subject Classification: 03C60, 03C10, 03C30

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Full text arXiv 2310.14363: pdf, ps.