Sylvy Anscombe
My research interests lie in Model Theory, a part of Mathematical Logic, including connections to algebra and number theory.

publications

submitted/notes
  1. Notes on tame valued fields.
    Manuscript, 2026. pdf
  2. Elimination results for tame fields with finite residue fields, with Blaise Boissonneau.
    Submitted, 2026. arXiv:2604.26129 [math.LO]
  3. On lambda functions in henselian and separably tame valued fields.
    Submitted, 2025. arXiv:2505.07518 [math.LO]
research articles
  1. Multidimensional asymptotic classes, with Dugald Macpherson, Charles Steinhorn, and Daniel Wolf.
    To appear in Transactions of the American Mathematical Society, 2026. arXiv:2408.00102 [math.LO]
  2. Existential fragments of theories of henselian valued fields, with Arno Fehm.
    Zeitschrift für Mathematische Logik und Grundlagen der Mathematik, 72:445–456, 2026.
    links arXiv:2601.17395 [math.LO] doi:10.60866/CAM.325
  3. Interpretations of syntactic fragments of theories of fields, with Arno Fehm.
    Israel Journal of Mathematics, 2026.
    links arXiv:2312.17616 [math.LO] doi:10.1007/s11856-026-2938-z
  4. One-dimensional $F$-definable sets in $F(\!(t)\!)$.
    Journal of Algebra, 687 (2026) 731–742.
    links arXiv:1503.05803 [math.LO] hal-05292948 doi:10.1016/j.jalgebra.2025.09.005
  5. Universal-existential theories of fields, with Arno Fehm.
    Proceedings of the Edinburgh Mathematical Society, 69(1):95–124, 2026.
    links arXiv:2405.12771 [math.LO] hal-05344752 doi:10.1017/S0013091525100771
  6. Ax–Kochen–Ershov principles for finitely ramified henselian fields, with Philip Dittmann and Franziska Jahnke.
    Transactions of the American Mathematical Society, 377-12:8963–8988, 2024.
    links arXiv:2305.12145 [math.LO] hal-05158062 doi:10.1090/tran/9271
  7. Characterizing NIP henselian fields, with Franziska Jahnke.
    Journal of the London Mathematical Society, 109(3), 2024.
    links arXiv:1911.00309 [math.LO] hal-05158057 doi:10.1112/jlms.12868
  8. Axiomatizing the existential theory of $\mathbb{F}_{q}(\!(t)\!)$, with Philip Dittmann and Arno Fehm.
    Algebra & Number Theory, 17-11:2013–2032, 2023.
    links arXiv:2205.05438 [math.LO] hal-05158056 doi:10.2140/ant.2023.17.2013
  9. The model theory of Cohen rings, with Franziska Jahnke.
    Confluentes Mathematici, 14, no. 2, 1–28, 2022.
    links arXiv:1904.08297 [math.LO] hal-05158048 doi:10.5802/cml.84
  10. Denseness results in the theory of algebraic fields, with Philip Dittmann and Arno Fehm.
    Annals of Pure and Applied Logic, 172(8):102973, 2021.
    links arXiv:1909.12188 [math.LO] doi:10.1016/j.apal.2021.102973
  11. A $p$-adic analogue of Siegel's theorem on sums of squares, with Philip Dittmann and Arno Fehm.
    Mathematische Nachrichten, 293:1434–1451, 2020.
    links arXiv:1904.03466 [math.NT] doi:10.1002/mana.201900173
  12. Approximation theorems for spaces of localities, with Philip Dittmann and Arno Fehm.
    Mathematische Zeitschrift, 296:1471–1499, 2020.
    links arXiv:1901.02632 [math.AC] doi:10.1007/s00209-020-02516-6
  13. Existentially generated subfields of large fields.
    Journal of Algebra, 517C:78–94, 2019.
    links arXiv:1710.03353 [math.LO] doi:10.1016/j.jalgebra.2018.09.021
  14. Henselianity in the language of rings, with Franziska Jahnke.
    Annals of Pure and Applied Logic, 169(9):872–895, 2018.
    links arXiv:1512.04588 [math.LO] doi:j.apal.2018.04.008
  15. Characterizing diophantine henselian valuation rings and valuation ideals, with Arno Fehm.
    Proceedings of the London Mathematical Society, 115:293–322, 2017.
    links arXiv:1602.01233 [math.LO] doi:10.1112/plms.12042
  16. Notes on extremal and tame valued fields, with Franz-Viktor Kuhlmann.
    Journal of Symbolic Logic, 81:400–416, 2016.
    links arXiv:1407.3759 [math.LO] doi:10.1017/jsl.2016.6
  17. The existential theory of equicharacteristic henselian valued fields, with Arno Fehm.
    Algebra & Number Theory, 10-3:665–683, 2016.
    links arXiv:1501.04522 [math.LO] doi:10.2140/ant.2016.10.665
  18. An existential $\emptyset$-definition of $\mathbb{F}_{q}[\![t]\!]$ in $\mathbb{F}_{q}(\!(t)\!)$, with Jochen Koenigsmann.
    Journal of Symbolic Logic, 79:1336–1343, 2014.
    links arXiv:1306.6760 [math.LO] doi:10.1017/jsl.2014.27
other publications
  1. A note on existentially t-henselian fields.
    To appear in proceedings of conference DDG40. arXiv:2603.27612 [math.LO]
  2. Exposé Bourbaki 1246 : The model theory of perfectoid fields [after Jahnke and Kartas].
    Séminaire Bourbaki, volume 2025/2026. To appear.
    links arXiv:2602.23779 [math.LO] video
  3. The unknown logic of power series.
    Notices of the American Mathematical Society, 71(11):1448–1455, 2024.
    links hal-05158080v1 doi:10.1090/noti3081
  4. A survey of local-global methods for Hilbert's Tenth Problem, with Valentijn Karemaker, Zeynep Kisakürek, Vlerë Mehmeti, Margherita Pagano, and Laura Paladino.
    Women in Numbers Europe IV, edited by Ramla Abdellatif, Valentijn Karemaker, and Lejla Smajlovic. Assoc. Women Math. Ser., 32, 29--61, Springer, Cham, 2024.
    links hal-05472571 doi:10.1007/978-3-031-52163-8_2
  5. Imperfection in NIP fields, with Franziska Jahnke.
    Extended abstract, Oberwolfach Reports (20) 2023, pp. 125–127.
    links doi:10.4171/OWR/2023/2
  6. Exposé Bourbaki 1186 : Shelah’s Conjecture and Johnson’s Theorem [after Will Johnson].
    Séminaire Bourbaki, volume 2021/2022, exposés 1181-1196. Astérisque, no.438, p. 247–279, 2022.
    links hal-05158075 doi:10.24033/ast.1187
theses
  1. Axiomatisabilité et décidabilité de corps valués henséliens. HDR Mémoire, Université Paris Cité, 2026.
    links tel-05477988 slides
  2. Definability in Henselian Fields. DPhil Thesis, University of Oxford, 2013.
    Supervised by Prof. Jochen Koenigsmann.
    links ora:65eec6d9-457d-4673-80de-6413865a6a46

research team

Postdoc PhD Master/Mémoire
  • Sol Susana Santoyo Olivera. Current student, co-supervised with Pablo Cubides Kovacsics, 2026.
  • Mahsa Yadegari Khozani. Non-definability of rings of integers, current student, 2026.
  • Xiaorui Yin. Globally valued fields, mémoire de M2, 2026.
  • Julie Plessis. Power series with cross-sections, current student, 2026.
  • Fares Arous. Separably algebraically maximal fields, current student, 2026.
  • Thibaud Oiffer. Measure and dimension in pseudofinite fields, mémoire de M1, 2026.
  • Fares Arous. Corps de Kaplansky très minces, mémoire de M1, 2025.
  • Fares Arous. Théorie des modèles du graphe de Rado, stage de L3, 2024.
  • Nolwen Chabaud. Théorie des modèles des corps valués, mémoire de M1, 2023.
  • Julien Delteil. Théorie des modèles des corps finis, stage de L3, 2023.
  • Paulo Andrés Soto Moreno. Inflators and diffeo-valued fields, mémoire de M2, 2022.
If you're interested in studying with me, please contact me.

editorial work

Currently serving as editor of

selected talks

  1. First-order theories of power series fields, Mathematical Colloquium, HHU Düsseldorf, June 2026.
  2. What can model theory say about power series fields? (plenary lecture), XXI Simposio Latinoamericano de Lógica Matemática (SLALM XXI), Bogotá, June 2026.
  3. Around tame fields: $\mathbb{F}_{q}(\!(\mathbb{Q})\!)$, eliminations, transfer, and beyond, A85: algebra and arithmetic from model theory, ICMS, Edinburgh, May 2026.
  4. La théorie des modèles des corps perfectoïdes [d'après Jahnke et Kartas], Séminaire N. Bourbaki, IHP, Paris, 31st January 2026.
  5. Sixty years of Ax–Kochen–Ershov transfer principles (abstract), Introductory School “Definability, decidability, and computability”, HIM, Bonn, September 2025.
  6. AKE in fragments for separably tame valued fields, Workshop on applications of model theory in combinatorics and valued fields, Singapore, June 2025.
  7. Universal-existential theories of henselian valued fields, and of function fields, DDC@Cambridge: FRG Workshop on Definability, Decidability, and Computability, Harvard, August 2024.
  8. Transfer of decidability for existential theories of (valued) fields (abstract, video), Théorie des modèles des corps valués, CIRM, Luminy, May 2023.
  9. Le Xème problème de Hilbert - un problème pour le XXème et le XXIème siècle (slides), Séminaire « Des mathématiques », ENS-Ulm, February 2023.
  10. Hilbert's Tenth Problem: between logic and number theory, Inaugural ASL Tutorial Lectures, JMM 2023, Boston, January 2023.
  11. Imperfection in NIP fields, Model Theory: Combinatorics, Groups, Valued Fields and Neostability, Mathematisches Forschungsinstitut Oberwolfach, January 2023.
  12. Existential AKE principles for henselian valued fields (video), Seminar, Decidability, definability and computability in number theory, Part 2, MSRI, July 2022.
  13. Henselian discretely valued fields and existential AKE principles (slides), Logic Colloquium 2022, Reykjavík, June 2022.
  14. Exposé Bourbaki 1186 : Shelah's Conjecture and Johnson’s Theorem [after Will Johnson] (notes), Séminaire N. Bourbaki, IHP, Paris, November 2021.

meetings (co-)organized


useful links