Undecidability and Definability for the Theory of Global Fields

DOI10.2307/1999979zbMath0472.03010OpenAlexW4237220814MaRDI QIDQ3926549

Robert S. Rumely

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/1999979

zbMATH Keywords

function fieldsvaluationspolynomial ringsnatural numbersHasse principleGoedel functions

Mathematics Subject Classification ID

Decidability (number-theoretic aspects) (11U05) Decidability and field theory (12L05) Decidability of theories and sets of sentences (03B25)

Related Items

Uniform first-order definitions in finitely generated fields, Definability of the ring of integers in some infinite algebraic extensions of the rationals, First-order decidability and definability of integers in infinite algebraic extensions of the rational numbers, Elementary equivalence versus isomorphism. II, A TOPOLOGICAL APPROACH TO UNDEFINABILITY IN ALGEBRAIC EXTENSIONS OF, Undecidability, unit groups, and some totally imaginary infinite extensions of ℚ, Hilbert's tenth problem for fields of rational functions over finite fields, THE ELEMENTARY THEORY OF LARGE FIELDS OF TOTALLY -ADIC NUMBERS, Endomorphisms of elliptic curves and undecidability in function fields of positive characteristic., Uniform existential interpretation of arithmetic in rings of functions of positive characteristic, Hilbert's tenth problem for rings of rational functions, Extensions of Hilbert’s Tenth Problem: Definability and Decidability in Number Theory, Recursively enumerable sets of polynomials over a finite field are Diophantine, A CLASS OF FIELDS WITH A RESTRICTED MODEL COMPLETENESS PROPERTY, Infinite finitely generated fields are biinterpretable with ℕ, Integrality at a prime for global fields and the perfect closure of global fields of characteristic \(p > 2\), Definability of the ring of integers in pro-\(p\) Galois extensions of number fields, First-order definitions of rational functions and \({\mathcal S}\)-integers over holomorphy rings of algebraic functions of characteristic 0, A construction of real closed fields, Uniformly defining \(p\)-Henselian valuations, Definability and decidability in infinite algebraic extensions, Relatively projective groups as absolute Galois groups

Cites Work

• The Undecidability of Algebraic Rings and Fields
• THE UNDECIDABILITY OF PURE TRANSCENDENTAL EXTENSIONS OF REAL FIELDS
• Definability and decision problems in arithmetic
• Undecidable Rings
• Arithmetical definability of field elements
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