Bonn Mathematical Logic Group

Philipp Hieronymi

Office: Room 4.005

Research interests

Teaching (SoSe24)


  1. 'Defining the set of integers in expansions of the real field by a closed discrete set',
    Proc. Amer. Math. Soc. 138 (2010) 2163-2168, pdf
  2. 'The real field with the rational points of an elliptic curve', with Ayhan Günaydin,
    Fund. Math. 211 (2011) 15-40, pdf
  3. 'Dependent pairs', with Ayhan Günaydin,
    J. Symb. Logic (2) 76 (2011) 377-390, pdf
  4. 'The real field with an irrational power function and a dense multiplicative subgroup',
    J. London Math. Soc. (2) 83 (2011) 153-167, pdf,
  5. 'Expansions of subfields of the real field by a discrete set',
    Fund. Math. 215 (2011) 167-175, pdf
  6. 'Expansions which introduce no new open sets', with Gareth Boxall,
    J. Symb. Logic (1) 77 (2012) 111-121, pdf
  7. 'A dichotomy for expansions of the real field', with Antongiulio Fornasiero and Chris Miller,
    Proc. Amer. Math. Soc. 141 (2013) 697-698, pdf
  8. 'An analogue of the Baire Category Theorem',
    J. Symb. Logic (1) 78 (2013) 207-213, pdf
  9. 'Interpreting the projective hierarchy in expansions of the real line', with Michael Tychonievich,
    Proc. Amer. Math. Soc. 142 (2014) 3259-3267, pdf
  10. 'A fundamental dichotomy for definably complete expansions of ordered fields', with Antongiulio Fornasiero,
    J. Symb. Logic (4) 80 (2015) 1091-1115 pdf
  11. 'Expansions of the ordered additive group of real numbers by two discrete subgroups',
    J. Symb. Logic (3) 81 (2016) 1007–1027 pdf
  12. 'Distal and non-distal pairs', with Travis Nell,
    J. Symb. Logic (1) 82 (2017) 375-383 pdf
  13. 'How to avoid a compact set' with Antongiulio Fornasiero and Erik Walsberg,
    Adv. Math. 317 (2017) 758-785 pdf
  14. 'Wild theories with o-minimal open core' with Travis Nell and Erik Walsberg,
    Ann. Pure Appl. Logic (2) 169 (2018) 146-163 pdf
  15. 'Ostrowski numeration systems, addition and finite automata', with Alonza Terry Jr,
    Notre Dame J. Formal Logic (2) 59 (2018) 215-232 pdf
  16. 'Interpreting the monadic second order theory of one successor in expansions of the real line', with Erik Walsberg,
    Israel J. Math. (1) 224 (2018) 39–55 pdf
  17. 'A tame Cantor set',
    J. European Math. Soc. (9) 20 (2018) pp. 2063–2104 pdf
  18. 'When is scalar multiplication decidable?',
    Ann. Pure Appl. Logic (2019) 1162-1175 pdf
  19. 'Metric dimensions and tameness in expansions of the real field' with Chris Miller,
    Trans. Amer. Math. Soc. (2) 373 (2020) 849-874 pdf
  20. 'An o-minimal trace that does not eliminate imaginaries' with P. Eleftheriou,
    Appendix to: 'Small sets in dense pairs' by P. Eleftheriou, Israel J. Math. 233 (2019) 1-27 pdf
  21. 'Structure theorems in tame expansions of o-minimal structures by a dense set' with Pantelis Eleftheriou and Ayhan Günaydin,
    Israel J. Math. 239 (2020) 435-500 pdf
  22. 'Continuous Regular Functions' with Alexi Block Gorman, Elliot Kaplan, Ruoyu Meng, Erik Walsberg, Zihe Wang, Ziqin Xiong and Hongru Yang,
    Log. Methods Comput. Sci. (1) 16 (2020) #17 pdf
  23. 'The Choice Property in tame expansions of o-minimal structures' with Pantelis Eleftheriou and Ayhan Günaydin,
    Math. Logic Quart. (2) 66 (2020) 239-246 pdf
  24. 'Pairs of Theories Satisfying a Mordell-Lang Condition' with Alexi Block Gorman and Elliot Kaplan,
    Fund. Math. (2) 251 (2020) 131-160 pdf
  25. 'Expansions of the real field by discrete subgroups of Gl_n(C)' with Erik Walsberg and Samantha Xu,
    Proc. Amer. Math. Soc. 149 (2021) 2221-2233 pdf
  26. 'Presburger Arithmetic with algebraic scalar multiplications ' with Danny Nguyen and Igor Pak,
    Log. Methods Comput. Sci. (3) 17 (2021) #4 pdf
  27. 'A tetrachotomy for expansions of the real ordered additive group' with Erik Walsberg,
    Sel. Math. New Ser. 27 (2021) #54 pdf,
    formerly: 'On continuous functions definable in expansions of the ordered real additive group'
  28. 'Pathological examples of structures with o-minimal open core' with Alexi Block Gorman and Erin Caulfield,
    Math. Logic Quart. (3) 67 (2021) 382-393 pdf
  29. 'Decidability for Sturmian words', with Dun Ma, Reed Oei, Luke Schaeffer, Chris Schulz and Jeffrey Shallit,
    Computer Science Logic (CSL) (2022) #24 pdf
  30. 'A strong version of Cobham's theorem', with Chris Schulz,
    ACM Symposium on Theory of Computing (STOC) (2022) 1172-1179 pdf
  31. 'Fractals and the monadic second order theory of one successor' with Erik Walsberg,
    J. Log. Anal. 15:5 (2023) 1-25 pdf
  32. 'Decidability bounds for Presburger arithmetic extended by sine' with Eion Blanchard,
    Ann. Pure Appl. Logic (2024) to appear pdf
  33. DPhil Thesis, 'The real field with an irrational power function and a dense multiplicative subgroup',
    ORA, Nov. 2008


  1. 'Definability and decidability in expansions by generalized Cantor sets' with William Balderrama, pdf
  2. 'Pecan: An Automated Theorem Prover for Automatic Sequences using Büchi Automata' with Reed Oei, Dun Ma and Christian Schulz, pdf


  1. 'The Clean-Development Mechanism, stochastic permit prices and energy investments' with David Schüller,
    Energy Economics 47 (2015) 25–36
  2. 'The Influence of Permit Price Uncertainty and Lobbying on Energy Investments' with David Schüller,
    in 'Emissions Trading as a Policy Instrument: Evaluation and Prospects', CESifo Seminar Series, MIT Press (2015) 87-120


  1. 'Geometry Labs United: An Invitation' with Jayadev Athreya, David Dumas, William Goldman,Sergey Grigorian, Rosemary Guzman, Sean Lawton, Anton Lukyanenko, Jeremy Tyson, and Aaron Wilson,
    Notices Amer. Math. Soc. (9) 65 (2018) 1088-1094, pdf
  2. 'Innovating and modernizing a Linear Algebra class through teaching computational skills', with Mariana Silva, Matthew West, Sascha Hilgenfeldt, Nicolas Nytko, Akshit Deshpande, and Jer-Chin Chuang,
    2022 ASEE Annual Conference & Exposition, Minneapolis, MN,, pdf

Work by students

  1. 'On expansions of the real field by complex subgroups', by Erin Caulfield,
    Ann. Pure Appl. Logic 168 (2017) 1308–1334 pdf
  2. 'Distal and non-Distal Behavior in Pairs', by Travis Nell,
    Math. Log. Quart. (1) 65 (2019) 23-36, pdf
  3. 'Companionability Characterization for the Expansion of an O-minimal Theory by a Dense Subgroup', by Alexi Block Gorman,
    Ann. Pure Appl. Logic (10) 174 (2023) 103316, pdf
  4. 'Undefinability of multiplication in Presburger arithmetic with sets of powers', by Chris Schulz, pdf



  1. Erik Walsberg, 2016-2019, first position: Postdoc UC Irvine
  2. Christian d'Elbée, 2022-2023, first position: Marie Curie Leeds
  3. Tingxiang Zou, since 2024

PhD students

  1. Erin Caulfield, graduated 2018, first position: Postdoc McMaster University
  2. Travis Nell, graduated 2019, first position: Data Scientist at Capital One
  3. Alexi Block Gorman, graduated 2021, first position: Postdoc Fields Institute
  4. Chris Schulz, graduated 2023, first position: Postdoc Waterloo
  5. Eion Blanchard, graduated 2023, first position: Postdoc MSRI
  6. Madie Farris, since 2020
  7. Leon Chini, since 2022
  8. Sven Manthe, since 2023
  9. Yilong Zhang, since 2023

Master students

  1. Xiaoduo Wang (2022), Quantifier elimination and decidability of the theory of additive integer group augmented by predicates of multiplicative cyclic submonoids, pdf (-> PhD student Manchester)
  2. Leo Gitin (2022), Decidability in expansions of local fields, pdf (-> DPhil student Oxford)
  3. Felix Jäger (2022), Towards a d-minimal Pila-Wilkie theorem, pdf
  4. Juan Sebastian Diaz Serrano (2023), Alpha-Presburger Arithmetic: Complexity and Axiomatization
  5. Sven Manthe (2023), An analogue of Cobham's theorem for scalar multiplication (-> PhD student Bonn)
  6. Yilong Zhang (2023), Green points in the real field (-> PhD student Bonn)
  7. Iñaki Garrido (2023), Linearity of type A expansions
  8. Carlos Urban Abengozar (2023), The zero set property in definably complete expansions of ordered fields
  9. Roman Feller (2023), A dichotomy for type A structures, pdf (-> PhD student Vienna)
  10. Kim Kiehn (2023), Complexity Theory in Expansions of Presburger Arithmetic (-> PhD student Stockholm)
  11. Frederik Gebert (2024), NIP Expansions of the Real Field

Bachelor students

  1. Carl Jacobsen (2022)
  2. Matthias Franz (2022)
  3. Lucas Valle Thiele (2022), The Pila-Zannier method for abelian varieties, pdf
  4. Simon Blasinski (2022)
  5. Thomas Freiherr von Campenhausen (2022)
  6. Antonia Westphal (2022)
  7. Sarah Zengl (2022)
  8. Johannes Dertmann (2022)
  9. Laura Caspers (2023), A structure with a weak pole that is not field-type, pdf
  10. Laura Khaze (2023)
  11. Fabian Schmitthenner (2023), Decidability Questions in Ostrowski Numeration Systems, pdf
  12. Darius Tenthoff (2023)

Graduate students (who participated in research projects)

  1. Pete Glaze (2010-2011)
  2. Nathan Rehfuss (2013-2014)
  3. Alonza Terry Jr. (2013-2016)
  4. William Balderrama (2016)
  5. Rocco Davino (2019-2021)
  6. Ran Ji (2020-2022)


Universität Bonn
Mathematisches Institut
Endenicher Allee 60
D-53115 Bonn