Undecidability in number theory

2013/09/02 by Jochen Koenigsmann, Koenigsmann, Jochen
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1309.0441

48 pages. arXiv admin note: text overlap with arXiv:1011.3424

arxiv created 2013/09/02 · arxiv updated 2013/09/03

Abstract

These lecture notes cover classical undecidability results in number theory, Hilbert's 10th problem and recent developments around it, also for rings other than the integers. It also contains a sketch of the authors result that the integers are universally definable in the rationals.

Citations

• Defining ℤ in ℚ

Related

• Remarks on undecidability of indecomposable polynomial rings
• Defining Integers
• Descent on Elliptic Curves and Hilbert's Tenth Problem
• First Order Decidability and Definability of Integers in Infinite Algebraic Extensions of Rational Numbers
• Hilbert's tenth problem, Gödel's incompleteness, Halting problem, a unifying perspective