Interpretations of syntactic fragments of theories of fields

2023/12/29 by Anscombe, Sylvy, Fehm, Arno · 1 citation
#12L05 03B25 12J20 03C60 12L05 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2312.17616

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.

Cited by

• Relative Quantifier Elimination for Separable-Algebraically Maximal Kaplansky Fields

Related

• Universal-existential theories of fields
• Ax-Kochen-Ershov principles for finitely ramified henselian fields
• Decidable Fragment of Theories in Field Arithmetic
• On the existential theory of the completions of a global field
• "Fields" in classical and quantum field theories