First-order decidability and definability of integers in infinite algebraic extensions of the rational numbers (Q1659540)

scientific article

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English	First-order decidability and definability of integers in infinite algebraic extensions of the rational numbers	scientific article

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instance of

scholarly article

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title

First-order decidability and definability of integers in infinite algebraic extensions of the rational numbers (English)

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author

Alexandra Shlapentokh

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published in

Israel Journal of Mathematics

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publication date

22 August 2018

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full work available at URL

https://arxiv.org/abs/1307.0743

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MaRDI profile type

MaRDI publication profile

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cites work

Fields of algebraic numbers with bounded local degrees and their properties

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Division-ample sets and the Diophantine problem for rings of integers

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Diophantine Sets Over Algebraic Integer Rings. II

0 references

Diophantine Sets over Some Rings of Algebraic Integers

0 references

Hilbert’s Tenth Problem: Relations with Arithmetic and Algebraic Geometry

0 references

Descent on elliptic curves and Hilbert’s tenth problem

0 references

Hilbert's tenth problem and Mazur's conjectures in complementary subrings of number fields

0 references

Q4317826

0 references

Definability of the ring of integers in some infinite algebraic extensions of the rationals

0 references

Defining $\mathbb Z$ in $\mathbb Q$

0 references

Q5612629

0 references

Diophantine undecidability in some rings of algebraic numbers of totally real infinite extensions of $\mathbb{Q}$

0 references

Arithmetic over the rings of all algebraic integers.

0 references

Ranks of twists of elliptic curves and Hilbert's tenth problem

0 references

Additional results to a theorem of Eisenträger and Everest

0 references

THE UNDECIDABILITY OF PURE TRANSCENDENTAL EXTENSIONS OF REAL FIELDS

0 references

Q4737473

0 references

Hilbert’s Tenth Problem and Mazur’s Conjecture for large subrings of $\mathbb {Q}$

0 references

Q3588162

0 references

Characterizing integers among rational numbers with a universal-existential formula

0 references

Diophantine definability of infinite discrete nonarchimedean sets and Diophantine models over large subrings of number fields

0 references

Q4414310

0 references

Definability and decision problems in arithmetic

0 references

The Undecidability of Algebraic Rings and Fields

0 references

Q5726694

0 references

On $L$-functions of elliptic curves and cyclotomic towers

0 references

Undecidability and Definability for the Theory of Global Fields

0 references

First-order definitions of rational functions and ${\mathcal S}$-integers over holomorphy rings of algebraic functions of characteristic 0

0 references

Diophantine definability and decidability in extensions of degree 2 of totally real fields

0 references

Elliptic curves retaining their rank in finite extensions and Hilbert's Tenth Problem for rings of algebraic numbers

0 references

Rings of algebraic numbers in infinite extensions of $\mathbb Q$ and elliptic curves retaining their rank

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ELLIPTIC CURVE POINTS AND DIOPHANTINE MODELS OF ℤ IN LARGE SUBRINGS OF NUMBER FIELDS

0 references

Q5807665

0 references

Elimination theory for the ring of algebraic integers.

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On the constructible numbers

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Definability of the ring of integers in pro-$p$ Galois extensions of number fields

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The undecidability of cyclotomic towers

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Identifiers

zbMATH Open document ID

1436.03204

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DOI

10.1007/s11856-018-1708-y

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Mathematics Subject Classification ID

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Mathematics(1 entry)

mardi Publication:1659540