INTERPRETING ARITHMETIC IN THE FIRST-ORDER THEORY OF ADDITION AND COPRIMALITY OF POLYNOMIAL RINGS

DOI10.1017/jsl.2019.21zbMath1454.03015OpenAlexW2944782421MaRDI QIDQ5195064

Javier Utreras

Publication date: 17 September 2019

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/jsl.2019.21

zbMATH Keywords

undecidabilitypolynomial ringslanguage of rings

Mathematics Subject Classification ID

Decidability and field theory (12L05) Undecidability and degrees of sets of sentences (03D35) Decidability of theories and sets of sentences (03B25) First-order arithmetic and fragments (03F30)

Related Items (1)

UNIFORM DEFINABILITY OF INTEGERS IN REDUCED INDECOMPOSABLE POLYNOMIAL RINGS

Cites Work

• Uniform positive existential interpretation of the integers in rings of entire functions of positive characteristic
• The laws of integer divisibility, and solution sets of linear divisibility conditions
• Definability in terms of the successor function and the coprimeness predicate in the set of arbitrary integers
• Answer to a problem raised by J. Robinson: The arithmetic of positive or negative integers is definable from successor and divisibility
• The Diophantine Problem for Addition and Divisibility
• The Diophantine Problem for Polynomial Rings and Fields of Rational Functions
• An analogue of Hilbert's tenth problem for p-adic entire functions
• Definability and decision problems in arithmetic
• Undecidable Rings
• A list of arithmetical structures complete with respect to the first-order definability
• The Woods-Erdős conjecture for polynomial rings
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