famigliaestate2010

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. For those interested, here is a short propaganda to the subject and to myself. Other intersting material can be found in this and other web pages here (in italian), here (also in italian...) and also here (in english, for those who knows already the basics of set theory)

Here is a link to the official website of the YSTW 2013 to be held in Oropa (Piemonte) in June 2013.




CV

In english

In italian

Prizes

Winner of the Kurt Gödel Research Prize Fellowship 2010, awarded in 2010 to support original research in the foundations of mathematics. Here you can find the slides of the conference I held in occasion of the ceremony award.

Winner of the premio Fubini 2010, awarded in 2010 to a young mathematician working in Italy in the fields of logic, geometry and algebra.

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

Papers and reviews

"Martin's maximum and tower forcing", Israel Journal of Mathematics, 23 pages, not yet assigned to an issue: coxviale.pdf

"Guessing models and generalized Laver diamond", Annals of Pure and Applied Logic, Annals of Pure and Applied Logic, volume 163 (2012), no. 11, 1660-1678: viale.pdf

"On the consistency strength of the proper forcing axioms" (with Christoph Weiss), Advances in Mathematics, Volume 228 (2011), no. 5, 2672-2687: viale_weiss.pdf

"On the mapping reflection principle MRP" The Bulletin of Symbolic Logic 15(3), 322-325, 2009: BSLMRPrevMV.pdf

"Some consequences of reflection on the approachability ideal" (with Assaf Sharon) Transactions of the American Mathematical Society 362, 4201-4212, 2009 : RAMVAS.pdf

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

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

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

"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

Preprints

"Category forcings, MM^{+++}, and generic absoluteness for strong forcing axioms", 60 pages: Universal-partial-orders.pdf

"Martin's maximum revisited", 31 pages: Martinmaximumrevisited.pdf

"Martin's maximum and tower forcing", accepted in the Israel Journal of Mathematics, 23 pages: coxviale.pdf

You might as well be interested in the following paper by Weiss also appearing in Annals of Pure and Applied Logic, 163 (2012), no. 11, 1710–1717: weiss.pdf

Slides of some of my 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.

Here are the slides of my talk in Luminy (october 2010) concerning the consistency strength of PFA.

Here are the slides of my talk in Oberwolfach (january 2011) concerning the notion of guessing model.

Here are the slides of my talk in Bologna (february 2011) where I give a brief account of Woodin's Omega-logic as I understood it.

Here are the revised version of the slides of my talk in Singapore (july 2011) where I give a brief account of an absoluteness results for the theory of H(\aleph_2) in models of strong forcing axioms.

Here are the the slides of my talk in Freiburg (june 2012) where I introduce a constructive approach to Woodin's results in Omega-logic and some absoluteness results for the theory of H(\omega_2) in models of strong forcing axioms.

Here are the the slides of my talk as plenary speaker in the annual north american metting of the ASL held in Waterloo - Canada (may 2013) where I first introduce the category of stationary set preseving forcings (with arrows given by complete embeddings with a stationary set preserving quotient), then present MM^{+++}, a strong form of Martin's maximum, as a density property of this category, and finally sketch a proof the generic absoluteness of the theory of the Chang model L(Ord^{\omega_1}) for models of ZFC+MM^{+++}+large cardinals.

Many inaccuracies may occur in the slides, caveat lector!


Some lecture notes

FORCING AXIOMS AND REFLECTION PRINCIPLES lecture notes taken by Giorgio Audrito on a Ph.D course I gave in spring 2012 on this topic.

THE OPEN COLORING AXIOM lecture notes taken by Gemma Carotenuto on a Ph.D course I gave in spring 2012 on this topic.


SEMINARS AND TALKS IN TORINO LOGIC GROUP


Torino set theory workshop 13th november 2010

Here you can download the slides of some talks (Bagaria, Cox, Friedman) in the set theory workshop we had in Torino the 13th of november 2010.

Here you can download the slides of some of the talks in logic we have in Torino

Some inaccuracies may occur in the slides, caveat lector!




STUDENTS MASTER THESIS

Giorgio Venturi: "Forcing axioms and cardinality of the continuum", master thesis: venturi.pdf

Giorgio Audrito: "Characterizations of set generic extensions", master thesis: audrito.pdf

Fiorella Guichardaz: "Limits of boolean algebras and boolean valued models", master thesis: guichardaz.pdf

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, nonché una serie di indicazioni bibliografiche su questi temi per lettori interessati ma non esperti. Sulla pagina web del professor Andretta trovate altro materiale relativo al corso di teoria degli insiemi per il 2010.

Logica per informatica

CORSO 2009-2010 DI LOGICA E MATEMATICA DISCRETA

Qui trovate il testo con la soluzione dell'esame di logica del 8/2/2010. Qui trovate il testo con la soluzione dell'esame di logica del 25/2/2010. Qui trovate il testo e qui le soluzioni degli esercizi di logica assegnati a natale 2009 per la preparazione dell'esame. Guardate anche la pagina web del professor Andretta per ulteriori esercizi, prove d'esame e soluzioni.

INFORMAZIONI SUI CORSI DI LOGICA PER INFORMATICA DEGLI ANNI PASSATI

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 sui corsi e sugli esami degli anni passati tra le quali i testi degli esami passati nonchè tutte le dispense utilizzate nel corso di logica dell'anno 2008/2009.

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