Bonn Mathematical Logic Group

Philipp Hieronymi

Office: Room 4.005

Research interests

Teaching (WS2022/23)


  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, Christian Schulz and Jeffrey Shallit,
    Computer Science Logic (CSL) (2022) #24 pdf
  30. 'A strong version of Cobham's theorem', with Christian Schulz,
    ACM Symposium on Theory of Computing (STOC) (2022) 1172-1179 pdf
  31. 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. 'Fractals and the monadic second order theory of one successor' with Erik Walsberg, pdf
  3. 'Pecan: An Automated Theorem Prover for Automatic Sequences using Büchi Automata' with Reed Oei, Dun Ma and Christian Schulz, pdf
  4. 'Decidability bounds for Presburger arithmetic extended by sine' with Eion Blanchard, 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

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, pdf



  1. Erik Walsberg, 2016-2019, first position: Postdoc UC Irvine
  2. Christian d'Elbée, since 2022

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. Christian Schulz, since 2018
  5. Eion Blanchard, since 2019
  6. Madie Farris, since 2020

Master students

  1. Xiaoduo Wang, graduated 2022
  2. Leo Gitin, graduated 2022

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