Submission date: 29 December 2023

Abstract:

We set up general machinery to study interpretations of fragments of theories. We then apply this to existential fragments of theories of fields, and especially of henselian valued fields. As an application we prove many-one reductions between various existential theories of fields. In particular we exhibit several theories of fields many-one equivalent to the existential theory of ℚ.

Mathematics Subject Classification: 12L05 03B25 12J20 03C60 12L05

Keywords and phrases:

Full text arXiv 2312.17616: pdf, ps.