Decidable Fragment of Theories in Field Arithmetic

2019/12/19 by Chun-Yu Lin, Lin, Chun-Yu
Computer Science · Mathematics · #03B25 (Primary) 03C60 #11U05 #12L05 (Secondary) #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1912.09155

openalex publication_date 2019/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we show that the ∃¹ ∀¹ theories of Hilbertian fields with charateristic 0 and perfect Hilbertian fields are both decidable. We also prove that the ∀¹ ∃¹ theories of Hilbertian fields with charateristic 0, Hilbertian fields, PAC fields with characteristic 0, and PAC fields are all decidable.

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