Teaching

Research

Publications:

1. (with Omar León Sánchez) On Ordinary Differentially Large Fields. Canadian Journal of Mathematics. 2025. ArXiv.
2. (with G. Bezhanishvili, J. Madden, M. A. Moshier, J. Walters-Wayland) Subfitness in distributive (semi)lattices. Semigroup Forum. 2025. ArXiv.
3. (with Igor Klep) A Model Theoretic Perspective on Matrix Rings. Mathematische Zeitschrift 309 (2025), no. 3, Paper No. 45. ArXiv.
4. (with Omar León Sánchez) Differentially Large Fields. Algebra & Number Theory, Vol. 18 (2024), No. 2, 249-280. ArXiv, Final preprint.
5. (with Omar León Sánchez) Differential Weil Descent. Communications in Algebra, vol. 50, no. 1, p.104-114 (2022). ArXiv.
6. (with Luck Darnière) Defining integer valued functions in rings of continuous definable functions over a topological field. J. Math. Log. 20 (2020), no. 3, 24 pp.
7. (with Max Dickmann and Niels Schwartz) Spectral Spaces. New Mathematical Monographs, vol. 35, 650 pages. Cambridge University Press. March 2019. Online ISBN: 9781316543870. Reviews
8. Model Theory of Modules, Algebras and Categories. Edited by Alberto Facchini, Lorna Gregory, Sonia L'Innocente, Marcus Tressl. Contemporary Mathematics, vol. 730.
9. On the strength of some topological lattices. Ordered Algebraic Structures and Related Topics, Contemporary Mathematics, vol. 697, Amer. Math. Soc., Providence, RI, 2017, pp. 325-347. Final Preprint
10. Logic Colloquium 2012. Edited by Uri Abraham, Lev Beklemishev, Paola D'Aquino, Marcus Tressl. Annals of Pure and Applied Logic. Volume 167, Issue 10, Pages 865-1028 (October 2016)
11. (with Tim Mellor) Non-axiomatizability of real spectra in L_∞λ. Annales de la Faculté des Sciences de Toulouse, Vol. XXI, no. Spécial, 2012, pp. 131--146
12. (with Salma Kuhlmann) Comparison of Exponential-Logarithmic and Logarithmic-Exponential series. Math. Logic Quarterly, 58, No. 6, 434 - 448 (2012).
13. (with Niels Schwartz) Elementary properties of minimal and maximal points in Zariski spectra. Journal of Algebra 323 (2010) 698-728.
14. Bounded super real closed rings. Logic Colloquium 2007, volume 35 of Lect. Notes Log., pages 220--237. Assoc. Symbol. Logic, La Jolla, CA, 2010.
15. Heirs of box types in polynomially bounded structures. The Journal of Symbolic Logic, vol 74, No. 4, p.1225-1263 (2009).
16. Super real closed rings. Fundamenta Mathematicae 194 (2007), no. 2, 121-177.
17. (with Igor Klep) The Prime Spectrum and the Extended Prime Spectrum of non commutative Rings. Algebras and Representation Theory (2007), vol. 10, no. 3, 257 -- 270.
18. Pseudo Completions and Completions in Stages of o-minimal structures. Arch. Math. Logic (2006), vol 45, no. 8, 983-1009.
19. Computation of the z-radical in C(X). Advances in Geometry 6 (2006), no. 1, 139-175.
20. The elementary theory of Dedekind cuts in polynomially bounded structures. Annals of Pure and Applied Logic, Volume 135, Issues 1-3, September 2005, Pages 113-134.
21. The uniform companion for large differential fields of characteristic 0. Transactions of the American Mathematical Society 357 (2005), no. 10, 3933-3951.
22. Valuation theoretic content of the Marker-Steinhorn Theorem. The Journal of Symbolic Logic, vol. 69, No. 1, p.91-93 (2004).
23. (with Vincent Astier) Axiomatization of local-global principles for pp-formulas in spaces of orderings. Arch. Math. Logic 44 (2005), no. 1, 77--95.
24. Model Completeness of o-minimal Structures expanded by Dedekind Cuts. Journal of Symbolic Logic 70 (2005), no. 1, pp. 29--60.
25. Proceedings of the RAAG Summer School Lisbon 2003: O-minimal Structures. Edited By Niels Schwartz and Marcus Tressl. Network RAAG (2005).
26. (with Thomas Grill and Manfred Knebusch) An existence theorem for systems of implicit differential equations Banach Center Publications, vol. 58, Warszawa 2002, p.75-77.
27. A Structure Theorem for Differential Algebras Banach Center Publications, vol. 58, Warszawa 2002, p.201-206. Final Preprint
28. The real spectrum of continuous definable functions in o-minimal structures. Séminaire de Structures Algébriques Ordonnées 1997-1998, No. 68, Mars 1999, p. 1-15.

Preprints and work in progress:

1. Interpreting formulas of divisible lattice ordered abelian groups. 2016. pdf
2. (with Nicolas Guzy) pd-adically closed rings. Extended abstract as published in Séminaire de Structures Algébriques Ordonnées 2008.
3. Decidability questions for real closed rings.

Thesis: Dedekind cuts in polynomially bounded, o-minimal expansions of real closed fields.

The list of my former PhD students may be found on Mathematics Genealogy Project

Other notes.

• C*-algebras. Self-contained exposition of the Gel'fand-Naimark-Segal construction.
• Gröbner bases. A quick reference.
• Characteristic sets in differential algebra. Detailed and self-contained introduction to Kolchin's approach in characteristic 0.
• Introduction to the Model Theory of Differentially Closed Fields. A postgraduate course.
• Introduction to Lattice Ordered Abelian Groups. A postgraduate course.
• Dedekind cuts of ordered abelian groups and fields. A starting point.
• Stone Duality for Boolean Algebras.
• Model Theory. An MSc course with an extended bibliography.
• Gödel's Incompleteness Theorems. An MSc course.
• Characterizations of Stable Formulas. A short postgraduate course.
• NIP. Self-contained introduction to dependent theories.
• O-minimal structures (with an application to neural network learning). Yet another introduction to o-minimality. With application to Neural Networking Learning.

Links