Matteo Viale

E-mail: matteo dot viale at unito dot it

Phone: + 39 - 011 - 670 2931

I currently got a permanent position as a researcher in the math department of the University of Torino. I got my PhD under the direction of Boban Velickovic, professor at the university of Paris 7, and Alessandro Andretta, professor at the university of Torino and then got a three year Post Doc position in the Kurt Gödel Research Center for Mathematical Logic of the University of Vienna.

My research interests lie in the area of mathematical logic, more specifically, in set theory; even more specifically: I'm interested in forcing axioms, large cardinals and singular cardinals combinatorics. For those interested, here is a short propaganda to the subject and to myself.

My Thesis, Papers, and Preprints

"Applications of the proper forcing axiom to cardinal arithmetic.": thesisMV.pdf
Sacks Prize for the best Ph.D. thesis in Mathematical Logic in 2006 attributed by the Association for Symbolic Logic.

"A binary modal logic for the intersection types of lambdacalculus." With Silvio Valentini. Information and Computation, 2003, volume 185, no. 2, 211--232: lambdaMV.pdf.

"The cumulative hierarchy and the constructible universe of ZFA." Mathematical Logic Quarterly, 2004, volume 50, no. 1, 99--103: zfaMV.pdf.

"The proper forcing axiom and the singular cardinal hypothesis." The Journal of Symbolic Logic, 2006, volume 71, no. 2, 473--479: proper-singularMV.pdf.

"A family of covering properties" Mathematical Research Letters, 2008, volume 15, no. 2, 221--238: CPMV.pdf.

"Forcing axioms, supercompact cardinals, singular cardinals combinatorics" The Bulletin of Symbolic Logic 14 (2008),no. 1, 99--113: BSLMV.pdf.

"Some consequences of reflection on the approachability ideal" to appear in Transactions of the American Mathematical Society. (12 pages): RAMVAS.pdf.

"On the mapping reflection principle MRP" to appear in the review section of The Bulletin of Symbolic Logic. (4 pages): BSLMRPrevMV.pdf.

CV

Here you can find my CV in English , in French and in Italian.

Slides of some talks

Here are the slides of my thesis defense (September 2006): A self contained proof of the singular cardinal hypothesis from the P-ideal dichotomy is presented.

Here are the slides of my talk in Bedlewo (July 2007) concerning saturation properties of models of strong forcing axioms.

Here are the slides of my talk in Bonn (January 2008) concerning the structure of the approachability ideal in models of Martin's Maximum.

Some inaccuracies may occur in the slides, caveat lector!

Corsi e materiale didattico

Teoria degli insiemi

Qui trovate una breve introduzione all'aritmetica cardinale e al problema del continuo, due dei temi più affascinanti in teoria degli insiemi, nonchè una serie di indicazioni bibliografiche su questi temi per lettori interessati ma non esperti. Qui trovate la pagina web relativa al corso di teoria degli insiemi per il 2010, se siete interessati a seguirlo scrivetemi.

Logica per informatica

Qui trovate una lista di testi di esame dei corsi di logica per informatica degli anni passati. Qui trovate la correzione del compito del 27/3/2009 versione A. Sulla pagina web del professor Andretta trovate molte altre informazioni utili sul corso e sugli esami tra le quali i testi degli esami finora svolti nonchè tutte le dispense utilizzate nel corso.