Luca Motto Ros

I currently work as assistant professor at the Logic Department of the University of Freiburg. Previously, I was a post-doc for three years (Oct 2007-Sep 2010) at the Kurt Gödel Research Center for Mathematical Logic (chair: Sy D. Friedman) at the University of Vienna. I got my PhD from the Polytechnic of Turin in 2007 under the direction of Riccardo Camerlo, professor at the Polytechnic of Turin, and Alessandro Andretta, professor at the University of Turin.

Research interests

Mathematical Logic, more specifically, Set Theory; even more specifically: Descriptive Set Theory, Wadge Theory, the Axiom of Determinacy and its consequences, Analytic Equivalence Relations and Quasi-orders.

Publications

Refereed Journals

• A new characterization of the Baire class 1 functions, Real Analysis Exchange 34 (2008/2009), no. 1, 29-48.
• Borel-amenable reducibilities for sets of reals, Journal of Symbolic Logic 74 (2009), no. 1, 27-49.
• A new proof of a theorem of Jayne and Rogers, joint work with Brian Semmes, Real Analysis Exchange 35 (2010), no. 1, 195-203.
• Baire reductions and good Borel reducibilities, Journal of Symbolic Logic 75 (2010), no. 1, 323-345.
• Beyond Borel-amenability: scales and superamenable reducibilities, Annals of Pure and Applied Logic 161 (2010), 829-836.
• Game representations of classes of piecewise definable functions, Mathematical Logic Quarterly 57 (2011), no.1, 95-112.
• Analytic equivalence relations and bi-embeddability, joint work with Sy-D. Friedman, Journal of Symbolic Logic 76 (2011), no. 1, 243-266.
• On the complexity of the relations of isomorphism and bi-embeddability, Proceedings of the American Mathematical Society 140 (2012), no. 1, 309-323.
• Invariantly universal analytic quasi-orders, joint work with Riccardo Camerlo and Alberto Marcone, accepted for publication on Transactions of the American Mathematical Society.
• Some observations on "A new proof of a theorem of Jayne and Rogers", joint work with Miroslav Kačena and Brian Semmes, accepted for publication on Real Analysis Exchange.

Preprints and papers in preparation

• The descriptive set-theoretical complexity of the embeddability relation on models of large size, preprint, submitted.
• Wadge-like reducibilities on arbitrary quasi-Polish spaces, joint work with Philipp Schlicht and Victor Selivanov, preprint, submitted.
• Souslin quasi-orders and definable cardinality, joint work with Alessandro Andretta, in preparation.
• A classification of \Delta^0_2-functions and a boundness theorem, in preparation.
• \omega-decomposable Borel functions, in preparation.

Others

• General reducibilities for sets of reals, PhD thesis at Polytechnic of Turin, 2007.
• Metodi effettivi in teoria degli insiemi: la topologia di Gandy-Harrington, undergraduate thesis at University of Turin, 2003.

Slides of some talks

• Here are the slides of my talk in the Set Theory special session of the Logic Colloquium 2011 held in Barcelona (July 2011) concerning the universality of the relation of embeddability among models of size a weakly compact cardinal.
• Here are the slides of my talk at the KGRC of Vienna (January 2010) concerning the relations of isomorphism and bi-embeddability.
• Here are the slides of my talk at the ESI workshop on large cardinals and descriptive set theory held in Vienna (June 2009) concerning (partial results on) invariantly universal analytic quasi-orders (partially joint work with Sy D. Friedman and Riccardo Camerlo).
• Here are the slides of my talk in Paris (December 2008) concerning analytic equivalence relations and bi-embeddability (joint work with Sy D. Friedman).
• Here are the slides of my talk in Amsterdam (August 2007) concerning Borel reducibilities for sets of reals (generalizations of the Wadge structure).

Curriculum Vitae

A short CV (in english) (last update: April 13 2012).

Teaching

• SS 2012:
  - Vorlesung "Descriptive Set Theory"
  - Seminar über Einbettungen und bessere Quasiordnungen
• WS 2011/2012:
  - Übungen zur Vorlesung "Logik für Studierende der Informatik" - Übungsblätter
  - Seminar über Forcingtechniken
• SS 2011:
  - Übungen zur Vorlesung "Axiomatische Mengenlehre" - Übungsblätter
  - Seminar "Borelmengen und Hierarchien"
• WS 2010/2011:
  - Seminar "Mengenlehre"
  - Seminar "Mengenlehre und Modelltheorie für Fortgeschrittene"

Links