Anscombe, Sylvy; Dittmann, Philip; Jahnke, Franziska Ax-Kochen-Ershov principles for finitely ramified Henselian fields. (English) Zbl 07937465 Trans. Am. Math. Soc. 377, No. 12, 8963-8988 (2024). MSC: 03C60 12L12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Anscombe, Sylvy; Karemaker, Valentijn; Kisakürek, Zeynep; Mehmeti, Vlerë; Pagano, Margherita; Paladino, Laura A survey of local-global methods for Hilbert’s tenth problem. (English) Zbl 07919511 Abdellatif, Ramla (ed.) et al., Women in numbers Europe IV. Research directions in number theory. Selected papers based on the presentations at the 4th workshop, WINE 4, Utrecht, the Netherlands, August 29 – September 2, 2022. Cham: Springer. Assoc. Women Math. Ser. 32, 29-61 (2024). MSC: 11U05 11G05 14G05 03B25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Anscombe, Sylvy; Dittmann, Philip; Fehm, Arno Axiomatizing the existential theory of \(\mathbb{F}_q((t))\). (English) Zbl 07783172 Algebra Number Theory 17, No. 11, 2013-2032 (2023). MSC: 03C60 11D88 11G25 12L05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Martínez-Ranero, Carlos; Utreras, Javier; Videla, Carlos R. Undecidability of \(\mathbb{Q}^{(2)} \). (English) Zbl 1455.11166 Proc. Am. Math. Soc. 148, No. 3, 961-964 (2020). Reviewer: Alexandra Shlapentokh (Greenville) MSC: 11U05 03B25 11R11 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fehm, Arno; Jahnke, Franziska Recent progress on definability of Henselian valuations. (English) Zbl 1388.12012 Broglia, Fabrizio (ed.) et al., Ordered algebraic structures and related topics. International conference at CIRM, Luminy, France, October 12–16, 2015. Proceedings. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-2966-9/pbk; 978-1-4704-4222-4/ebook). Contemporary Mathematics 697, 135-143 (2017). MSC: 12J10 12L12 03C60 12E30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Anscombe, Sylvy; Fehm, Arno Characterizing Diophantine Henselian valuation rings and valuation ideals. (English) Zbl 1436.03192 Proc. Lond. Math. Soc. (3) 115, No. 2, 293-322 (2017). Reviewer: Alexandra Shlapentokh (Greenville) MSC: 03C60 03C40 11D88 11U09 12J10 12L12 14G05 14G20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Korec, I. A list of arithmetical structures complete with respect to the first-order definability. (English) Zbl 0971.03035 Theor. Comput. Sci. 257, No. 1-2, 115-151 (2001). MSC: 03C07 11U05 03B10 11B65 03B25 × Cite Format Result Cite Review PDF Full Text: DOI
Denef, J. The Diophantine problem for polynomial rings and fields of rational functions. (English) Zbl 0399.10048 Trans. Am. Math. Soc. 242, 391-399 (1978). MSC: 11U05 03B25 11C08 13F20 × Cite Format Result Cite Review PDF Full Text: DOI