This topic focusses on model theory and its applications in group theory and algebraic geometry, as well as on inner model theory and forcing axioms. Central to our research on model theory are the classification of groups or fields under model-theoretic assumptions. The interplay of the axiom of determinacy with large cardinal hypotheses and strong hypotheses which settle prominent combinatorial statements is studied in our research on set theory.
$\bullet $ Sylvy Anscombe and Franziska Jahnke. Characterizing NIP henselian fields. Journal of the London Mathematical Society, March 2024. doi:10.1112/jlms.12868.
$\bullet $ David Kerr and Robin Tucker-Drob. Dynamical alternating groups, stability, property Gamma, and inner amenability. Annales scientifiques de l'École Normale Supérieure, 56(1):59–90, July 2023. doi:10.24033/asens.2528.
$\bullet $ Franziska Jahnke. Henselian expansions of NIP fields. Journal of Mathematical Logic, April 2023. doi:10.1142/s021906132350006x.
$\bullet $ Eusebio Gardella, Shirly Geffen, Julian Kranz, and Petr Naryshkin. Classifiability of crossed products by nonamenable groups. J. Reine Angew. Math., 797(0):285–312, April 2023. doi:10.1515/crelle-2023-0012.
$\bullet $ Franziska Jahnke and Konstantinos Kartas. Beyond the Fontaine-Wintenberger theorem. arXiv e-prints, April 2023. arXiv:2304.05881.
$\bullet $ David Asperó and Ralf Schindler. Martin's Maximum++ implies Woodin's axiom (∗). Ann. Math., 193(3):793–835, May 2021. doi:10.4007/annals.2021.193.3.3.
$\bullet $ Isabel Müller and Katrin Tent. Building-like geometries of finite Morley rank. J. Eur. Math. Soc. (JEMS), 21(12):3739–3757, August 2019. doi:10.4171/jems/912.
$\bullet $ Eliyahu Rips and Katrin Tent. Sharply 2-transitive groups of characteristic 0. J. Reine Angew. Math., 2019(750):227–238, May 2019. doi:10.1515/crelle-2016-0054.
$\bullet $ Aleksandra Kwiatkowska and Maciej Malicki. Automorphism groups of countable structures and groups of measurable functions. Israel J. Math., 230(1):335–360, March 2019. doi:10.1007/s11856-018-1825-7.
Back to top$\bullet $ Benjamin Brück, Kevin I Piterman, and Volkmar Welker. The Common Basis Complex and the Partial Decomposition Poset. International Mathematics Research Notices, August 2024. doi:10.1093/imrn/rnae177.
$\bullet $ Benjamin Brück. (non-)Vanishing of high-dimensional group cohomology. arXiv e-prints, April 2024. arXiv:2404.15026.
$\bullet $ Dugald Macpherson and Katrin Tent. Omega-categorical pseudofinite groups. arXiv e-prints, March 2024. arXiv:2403.17684.
$\bullet $ Sylvy Anscombe and Franziska Jahnke. Characterizing NIP henselian fields. Journal of the London Mathematical Society, March 2024. doi:10.1112/jlms.12868.
$\bullet $ Włodzimierz J. Charatonik, Aleksandra Kwiatkowska, Robert P. Roe, and Shujie Yang. Projective fraïssé limits of trees with confluent epimorphisms. arXiv e-prints, December 2023. arXiv:2312.16915.
$\bullet $ Stefan Hoffeler, Paul Larson, Ralf Schindler, and Liuzhen Wu. PFA and the definability of the nonstationary ideal. arXiv e-prints, October 2023. arXiv:2310.13784.
$\bullet $ Anna-Maria Ammer and Katrin Tent. On the model theory of open generalized polygons. arXiv e-prints, August 2023. arXiv:2308.03677.
$\bullet $ David Kerr and Robin Tucker-Drob. Dynamical alternating groups, stability, property Gamma, and inner amenability. Annales scientifiques de l'École Normale Supérieure, 56(1):59–90, July 2023. doi:10.24033/asens.2528.
$\bullet $ Philip Dittmann, Franziska Jahnke, Lothar Sebastian Krapp, and Salma Kuhlmann. Definable valuations on ordered fields. Model Theory, 2(1):101–120, June 2023. doi:10.2140/mt.2023.2.101.
$\bullet $ Stefan Hoffelner, Paul Larson, Ralf Schindler, and Liuzhen Wu. Forcing axioms and definability of the nonstationary ideal on ω1. The Journal of Symbolic Logic, pages 1–21, June 2023. doi:10.1017/jsl.2023.40.
$\bullet $ Sylvy Anscombe, Philip Dittmann, and Franziska Jahnke. Ax-Kochen-Ershov principles for finitely ramified henselian fields. arXiv e-prints, May 2023. arXiv:2305.12145.
$\bullet $ Franziska Jahnke. Henselian expansions of NIP fields. Journal of Mathematical Logic, April 2023. doi:10.1142/s021906132350006x.
$\bullet $ Eusebio Gardella, Shirly Geffen, Julian Kranz, and Petr Naryshkin. Classifiability of crossed products by nonamenable groups. J. Reine Angew. Math., 797(0):285–312, April 2023. doi:10.1515/crelle-2023-0012.
$\bullet $ Franziska Jahnke and Konstantinos Kartas. Beyond the Fontaine-Wintenberger theorem. arXiv e-prints, April 2023. arXiv:2304.05881.
$\bullet $ Agatha Atkarskaya, Eliyahu Rips, and Katrin Tent. The Burnside problem for odd exponents. arXiv e-prints, April 2023. arXiv:2303.15997.
$\bullet $ David Asperó and Ralf Schindler. Wieviele reelle Zahlen gibt es? Mathematische Semesterberichte, 70(1):1–15, March 2023. doi:10.1007/s00591-022-00331-0.
$\bullet $ Dan Segal and Katrin Tent. Defining $r$ and $g(r)$. Journal of the European Mathematical Society, 25(8):3325–3358, 2023. doi:10.4171/jems/1255.
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Investigators: Brück, Geffen, Jahnke, Kerr, Kwiatkowska, Tent
In this unit we investigate the algebraicity conjecture, which states that $\omega$-stable simple infinite groups are algebraic groups over algebraically closed fields, or the stable fields conjecture, which states that every infinite stable field is separably closed, and other classification conjectures under model-theoretic assumptions. Automorphism groups of homogeneous structures form a natural connection to descriptive set theory, ergodic theory and C*-algebras.
Investigators: De Bondt, Schindler, Winter
Recent insights into the interplay of the axiom of deteminacy with large cardinal hypotheses and strong hypotheses which settle prominent combinatorial statements have opened the door for a better understanding of that interplay. They have at the same time produced scenarios for further research on a new class of strong Chang-type models of determinacy and the potential to force strong fragments of Martin’s Maximum by ${\mathbb P}_{\rm max}$ style forcings over them.