Galois groups of large simple fields
A Pillay, E Walsberg - Model Theory, 2023 - msp.org
Suppose that K is an infinite field which is large (in the sense of Pop) and whose first-order
theory is simple. We show that K is bounded, namely has only finitely many separable …
theory is simple. We show that K is bounded, namely has only finitely many separable …
A Survey of Local–Global Methods for Hilbert's Tenth Problem
S Anscombe, V Karemaker, Z Kisakürek… - Women in Numbers …, 2024 - Springer
Abstract Hilbert's Tenth Problem (H10) for a ring R asks for an algorithm to decide correctly,
for each f∈ ℤ [X 1,…, X n], whether the diophantine equation f (X 1,…, X n)= 0 has a solution …
for each f∈ ℤ [X 1,…, X n], whether the diophantine equation f (X 1,…, X n)= 0 has a solution …
[PDF][PDF] On the existential theory of the completions of a global field
P Dittmann, A Fehm - arXiv preprint arXiv:2401.11930, 2024 - arxiv.org
arXiv:2401.11930v1 [math.LO] 22 Jan 2024 Page 1 arXiv:2401.11930v1 [math.LO] 22 Jan 2024
ON THE EXISTENTIAL THEORY OF THE COMPLETIONS OF A GLOBAL FIELD PHILIP …
ON THE EXISTENTIAL THEORY OF THE COMPLETIONS OF A GLOBAL FIELD PHILIP …
Approximation theorems for spaces of localities
S Anscombe, P Dittmann, A Fehm - Mathematische Zeitschrift, 2020 - Springer
Abstract The classical Artin–Whaples approximation theorem allows to simultaneously
approximate finitely many different elements of a field with respect to finitely many pairwise …
approximate finitely many different elements of a field with respect to finitely many pairwise …
Undecidability of infinite towers of Kummer extensions of
C Martinez-Ranero, J Utreras - arXiv preprint arXiv:2410.22947, 2024 - arxiv.org
We prove, assuming resolution of singularities in positive characteristic, an analogue of
Siegel's theorem on sum of squares in positive characteristic. The method of proof combines …
Siegel's theorem on sum of squares in positive characteristic. The method of proof combines …
Denseness results in the theory of algebraic fields
S Anscombe, P Dittmann, A Fehm - Annals of Pure and Applied Logic, 2021 - Elsevier
Denseness results in the theory of algebraic fields - ScienceDirect Skip to main contentSkip to
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[PDF][PDF] Undecidability of infinite towers of Kummer extensions of Fp (t)
C Martınez-Ranero, J Utreras - 2024 - researchgate.net
We prove, assuming resolution of singularities in positive characteristic, an analogue of
Siegel's theorem on sum of squares in positive characteristic. The method of proof combines …
Siegel's theorem on sum of squares in positive characteristic. The method of proof combines …
Galois groups of large fields with simple theory (with an appendix by Philip Dittmann)
A Pillay, E Walsberg - arXiv preprint arXiv:2011.10018, 2020 - arxiv.org
Suppose that $ K $ is an infinite field which is large (in the sense of Pop) and whose first
order theory is simple. We show that $ K $ is {\em bounded}, namely has only finitely many …
order theory is simple. We show that $ K $ is {\em bounded}, namely has only finitely many …