Teaching

Research

Publications:

1. (with Niels Schwartz) Elementary properties of minimal and maximal points in Zariski spectra. Journal of Algebra 323 (2010) 698-728.
2. Bounded super real closed rings. Lecture Notes in Logic 35, p. 220-237 (2010).
3. Heirs of box types in polynomially bounded structures. The Journal of Symbolic Logic, vol 74, No. 4, p.1225-1263 (2009).
4. Super real closed rings. Fundamenta Mathematicae 194 (2007), no. 2, 121-177.
5. (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.
6. Pseudo Completions and Completions in Stages of o-minimal structures. Arch. Math. Logic (2006), vol 45, no. 8, 983-1009.
7. Computation of the z-radical in C(X). Advances in Geometry 6 (2006), no. 1, 139-175.
8. 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.
9. The uniform companion for large differential fields of characteristic 0. Transactions of the American Mathematical Society 357 (2005), no. 10, 3933-3951.
10. Valuation theoretic content of the Marker-Steinhorn Theorem. The Journal of Symbolic Logic, vol. 69, No. 1, p.91-93 (2004).
11. (with Vincent Astier) Axiomatization of local-global principles for pp-formulas in spaces of orderings. Arch. Math. Logic 44 (2005), no. 1, 77--95.
12. Model Completeness of o-minimal Structures expanded by Dedekind Cuts. Journal of Symbolic Logic 70 (2005), no. 1, pp. 29--60.
13. (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.
14. A Structure Theorem for Differential Algebras. Banach Center Publications, vol. 58, Warszawa 2002, p.201-206.
15. 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 Salma Kuhlmann) A note on exponential-logarithmic and logarithmic-exponential power series fields.
2. (with Niels Schwartz) Boolean factor spaces of Zariski spectra.
3. (with Nicolas Guzy) pd-adically closed rings.
4. (with Tim Mellor) Non-axiomatizability of real spectra in $L_{\kappa,\omega }$.
5. Decidability questions for real closed rings.

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

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