2025/05/12 by Paulo Andrés Soto Moreno, Moreno, Paulo Andrés Soto
Mathematics · #03C10 #03C60 #12L12 #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Logic (math.LO)
paper · pdf · doi:10.48550/arxiv.2505.07418
openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03
Let C be the class of separable-algebraically maximal equi-characteristic Kaplansky fields of a given imperfection degree, admitting an angular component map. We prove that the common theory of the class C resplendently eliminates quantifiers down to the residue field and the value group, in a three sorted language of valued fields with a symbol for an angular component map and symbols for the parameterized lambda-functions. As a consequence, we obtain that equi-characteristic NIP and NIPn henselian fields with an angular component map resplendently eliminate field quantifiers in this language. We also prove that this elimination reduces existential formulas to existential formulas without quantifiers from the home sort. Finally, we draw several conclusions following the AKE philosophy for elements of the class C, including the usual AKE principles for ≡,≡∃,\preceq,\preceq∃ and for relative decidability.