Teaching

Research

Publications:

1. (with Tim Mellor) Non-axiomatizability of real spectra in L_∞λ. To appear in Annales de la Faculté des Sciences de Toulouse.
2. (with Niels Schwartz) Elementary properties of minimal and maximal points in Zariski spectra. Journal of Algebra 323 (2010) 698-728.
3. Bounded super real closed rings. Logic Colloquium 2007, volume 35 of Lect. Notes Log., pages 220--237. Assoc. Symbol. Logic, La Jolla, CA, 2010.
4. Heirs of box types in polynomially bounded structures. The Journal of Symbolic Logic, vol 74, No. 4, p.1225-1263 (2009).
5. Super real closed rings. Fundamenta Mathematicae 194 (2007), no. 2, 121-177.
6. (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.
7. Pseudo Completions and Completions in Stages of o-minimal structures. Arch. Math. Logic (2006), vol 45, no. 8, 983-1009.
8. Computation of the z-radical in C(X). Advances in Geometry 6 (2006), no. 1, 139-175.
9. 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.
10. The uniform companion for large differential fields of characteristic 0. Transactions of the American Mathematical Society 357 (2005), no. 10, 3933-3951.
11. Valuation theoretic content of the Marker-Steinhorn Theorem. The Journal of Symbolic Logic, vol. 69, No. 1, p.91-93 (2004).
12. (with Vincent Astier) Axiomatization of local-global principles for pp-formulas in spaces of orderings. Arch. Math. Logic 44 (2005), no. 1, 77--95.
13. Model Completeness of o-minimal Structures expanded by Dedekind Cuts. Journal of Symbolic Logic 70 (2005), no. 1, pp. 29--60.
14. (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.
15. A Structure Theorem for Differential Algebras. Banach Center Publications, vol. 58, Warszawa 2002, p.201-206.
16. 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. (with Nicolas Guzy) pd-adically closed rings. Extended abstract as published in Séminaire de Structures Algébriques Ordonnées 2008.
2. (with Salma Kuhlmann) Comparison of Exponential-Logarithmic and Logarithmic-Exponential series.
3. Decidability questions for real closed rings.
4. Spectral spaces. Book in preparation, jointly with Max Dickmann and Niels Schwartz.

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

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