Existential definability and diophantine stability
B Mazur, K Rubin, A Shlapentokh - Journal of Number Theory, 2024 - Elsevier
Let K be a number field, let L be an algebraic (possibly infinite degree) extension of K, and
let OK⊂ OL be their rings of integers. Suppose A is an abelian variety defined over K such …
let OK⊂ OL be their rings of integers. Suppose A is an abelian variety defined over K such …
Universal-existential theories of fields
S Anscombe, A Fehm - arXiv preprint arXiv:2405.12771, 2024 - arxiv.org
We study various universal-existential fragments of first-order theories of fields, in particular
of function fields and of equicharacteristic henselian valued fields. For example we discuss …
of function fields and of equicharacteristic henselian valued fields. For example we discuss …
Interpretations of syntactic fragments of theories of fields
S Anscombe, A Fehm - arXiv preprint arXiv:2312.17616, 2023 - arxiv.org
We set up general machinery to study interpretations of fragments of theories. We then apply
this to existential fragments of theories of fields, and especially of henselian valued fields. As …
this to existential fragments of theories of fields, and especially of henselian valued fields. As …
Universally defining finitely generated subrings of global fields
N Daans - Documenta Mathematica, 2021 - ems.press
Universally Defining Finitely Generated Subrings of Global Fields Page 1 Documenta Math.
1851 Universally Defining Finitely Generated Subrings of Global Fields Nicolas Daans …
1851 Universally Defining Finitely Generated Subrings of Global Fields Nicolas Daans …
Universally defining ZZ in QQ with 10 quantifiers
N Daans - Journal of the London Mathematical Society, 2024 - Wiley Online Library
Universally defining Z$\mathbb {Z}$ in Q$\mathbb {Q}$ with 10 quantifiers - Daans - 2024 -
Journal of the London Mathematical Society - Wiley Online Library Skip to Article Content Skip …
Journal of the London Mathematical Society - Wiley Online Library Skip to Article Content Skip …
Notes on the DPRM property for listable structures
H Pasten - The Journal of Symbolic Logic, 2022 - cambridge.org
A celebrated result by Davis, Putnam, Robinson, and Matiyasevich shows that a set of
integers is listable if and only if it is positive existentially definable in the language of …
integers is listable if and only if it is positive existentially definable in the language of …
First-order definability of Darmon points in number fields
JP De Rasis, H Handley - arXiv preprint arXiv:2410.03033, 2024 - arxiv.org
For a given number field $ K $, we give a $\forall\exists\forall $-first order description of affine
Darmon points over $\mathbb {P}^ 1_K $, and show that this can be improved to a …
Darmon points over $\mathbb {P}^ 1_K $, and show that this can be improved to a …
First-order definability of affine Campana points in the projective line over a number field
JP De Rasis - arXiv preprint arXiv:2401.16354, 2024 - arxiv.org
We offer a $\forall\exists $-definition for (affine) Campana points over $\mathbb {P}^ 1_K
$(where $ K $ is a number field), which constitute a set-theoretical filtration between $ K …
$(where $ K $ is a number field), which constitute a set-theoretical filtration between $ K …
is diophantine over with 32 unknowns
GR Zhang, ZW Sun - arXiv preprint arXiv:2104.02520, 2021 - arxiv.org
In 2016 J. Koenigsmann refined a celebrated theorem of J. Robinson by proving that
$\mathbb Q\setminus\mathbb Z $ is diophantine over $\mathbb Q $, ie, there is a polynomial …
$\mathbb Q\setminus\mathbb Z $ is diophantine over $\mathbb Q $, ie, there is a polynomial …
[PDF][PDF] Accepted by Bull. Pol. Acad. Sci. Math. See also arXiv: 2104.02520. Q\Z IS DIOPHANTINE OVER Q WITH 32 UNKNOWNS
GRUI ZHANG, Z SUN - maths.nju.edu.cn
In 2016 J. Koenigsmann refined a celebrated theorem of J. Robinson by proving that Q\Z is
diophantine over Q, ie, there is a polynomial P (t, x1,..., xn)∈ Z [t, x1,..., xn] such that for any …
diophantine over Q, ie, there is a polynomial P (t, x1,..., xn)∈ Z [t, x1,..., xn] such that for any …