The group focuses on the study of mathematical logic and its interaction with  other areas of mathematics and theoretical computer science.

ERC Research Sectors: PE1_1 Logic and foundations

Research areas: Set theory and its applications. Model theory. In particular: forcing and its applications, large cardinals and absoluteness, definability and complexity of classification problems, stability theory and its generalizations

Visits abroad (one month or more)

Raphaël Carroy, January 31st - March 2nd, 2018: Invited research stay, UCLA (USA) Host: Andrew Marks.

Collaborations with external institutions

Albert-Ludwigs-Universität Freiburg, Germany
Rheinische Friedrich-Wilhelms-Universität Bonn, Germany
University of Warsaw, Poland
University of Genoa, Italy
University of Udine, Italy
Kurt Gödel Research Center for Mathematical logic, Vienna, Austria
University of Lausanne, Switzerland
University of Norwich, United Kingdom
University of Campinas, Brasil
University Paris 7, France

Weekly seminars

Logic Seminars
Student seminars

Advanced Courses

Generalized Descriptive Set Theory (L. Motto Ros)
Iterated Forcing (M.Viale)

Workshops at the University of Torino

Convegno nazionale "Educare alla razionalità - L'insegnamento della matematica e della logica nella scuola secondaria" - May 22-23, 2019
Descriptive Set Theory Day in Torino - June 12th, 2018
Workshop on Wadge Theory and Automata II - June 8th, 2018
IIIM 2018 - Incontro Italiano Insiemi e Modelli 2018 - February 21-23, 2018

Research grants

Local Research Project — Progetti di Ricerca finanziati dall’Università di Torino (ex 60%) 2019, linea B
PRIN 2014: "Logica, Modelli e Insiemi"

Invited talks and seminars

Raphaël Carroy

Some graph dichotomies and some applications, 15th International Luminy Workshop in Set Theory, Marseille (Francia), 23.9.2019
Bases for Borel functions, XX Congresso dell'Unione Matematica Italiana, Pavia (Italia), 5.9.2019
The Open Graph Dichotomy and the second level of the Borel hierarchy, Joint meeting of the Italian Mathematical Union, the SIMAI and the Polish Mathematical Society, Wroclaw (Poland), 18.9.2018
Around finite basis results for topological embeddability between functions, Measuring the Complexity of Computational Content: From Combinatorial Problems to Analysis, Dagstuhl, Germany, 7.9.2018

Gianluca Paolini

First-Order Model Theory of Free Projective Planes, Logic Colloquium 2019, special session “Foundations of Geometry”. Prague, Czech Republic, 11-16.08.19.
First-Order Model Theory of Free Projective Planes, Joint Meeting of the Italian Mathematical Union, the SIMAI and the Polish Mathematical Society, Wrocław, Poland, 17-20.09.18.
On the Admissibility of a Polish Group Topology and some Results in Reconstruction Theory, Logic Colloquium 2018, special session “Model Theory”. Udine, Italy, 23-28.07.18.
On the Admissibility of a Polish Group Topology and Other Things, Young Set Theory Workshop 2018, Bernoulli Center, Lausanne, Switzerland, 25-29.6.18.
Automorphisms Groups and Reconstruction Problems, Set Theory, Model Theory and Applications (in memory of Mati Rubin). Eilat, Israel, 22-26.04.18.
Automorphisms Groups and Reconstruction Problems, Incontro Italiano Modelli e Insiemi 2018, Torino, Italy, 21-23.02.18.

Visits abroad (one month or more)

Alessandro Andretta, August 18th - September 24th, 2015, Isaac Newton institute special programme: Mathematical, Foundational and Computational Aspects of the Higher Infinite, Cambridge (UK)
Matteo Viale, November 1st - December 21st, 2015, Isaac Newton institute special programme: Mathematical, Foundational and Computational Aspects of the Higher Infinite, Cambridge (UK)

Collaborations with external institutions

Albert-Ludwigs-Universität Freiburg, Germany
Rheinische Friedrich-Wilhelms-Universität Bonn, Germany
University of Warsaw, Poland
A.P. Ershov Institute of Informatics Systems, Russian Academy of Sciences, Siberian Branch, Novosibirsk, Russia
Polytechnic of Turin, Italy
University of Udine, Italy
Kurt Gödel Research Center for Mathematical logic, Vienna, Austria
University of York, Canada
University of Bern, Switzerland
University of Lausanne, Switzerland
University of Norwich, United Kingdom
University of Campinas, Brasil

Weekly seminars

Logic Seminars
Student seminars

Advanced Courses

The axiom of determinacy and large cardinals (A. Andretta), at the University of Naples

Workshops at the University of Torino

Descriptive Set Theory in Turin - September 6-8, 2017
P.O.I Workshop in Pure and Descriptive Set Theory - September 25-26, 2015
Wadge theory and Automata - January 28th, 2015

Research grants

Young researchers grant "Rita Levi Montalcini" 2012: "New Advances in Descriptive Set Theory"
Local Research Project — Progetti di Ricerca finanziati dall’Università di Torino (ex 60%) 2015, linea A: “Modelli e Insiemi”
PRIN 2014: "Logica, Modelli e Insiemi"
PRIN 2013: "New Perspectives On The Nature of Infinity"

Invited talks and seminars

Alessandro Andretta

Descriptive set theory and the density function, Third Arctic Set Theory Meeting, Kilpisjärvi (Finland), 28.1.2017
Descriptive set theory and the density point property, Lausanne (Switzerland) 21.11.2015

Matteo Viale

An overview on category forcings, 14th International Workshop in Set Theory, CIRM-Luminy (Francia), 13-10-2017
Useful Axioms, SETTOP 2016, Fruska Gora (Serbia), 24/6/2016
Useful Axioms, IRP On Large Cardinals And Strong Logics, Workshop 1: Set-theoretical aspects of the model theory of strong logics, Barcelona (Spain), 30-9-2016
Systems of Filters, MM+70, Jerusalem (Israel), 19-2-2016
Category forcing axioms and generic absoluteness for third order arithmetic, Workshop: Independence Results in Mathematics and Challenges in Iterated Forcing, University of East Anglia, Norwich (UK), 3.11.2015
Problemi indecidibili in Matematica --- Cosa può dire al riguardo la teoria degli insiemi? XX congresso UMI, Siena, Italy, 9.9.2015.
Forcing as a tool to prove theorems: an example around Schanuel's conjecture, COMFORT, Pisa (Italy), 22/23-5-2015

Visits abroad (one month or more)

Matteo Viale, October 16th 2012 — November 18th 2012: special semester on "Forcing and its applications", Fields Institute, Toronto, Canada

Collaborations with external institutions

Albert-Ludwigs-Universität Freiburg, Germany
Rheinische Friedrich-Wilhelms-Universität Bonn, Germany
University of Warsaw, Poland
A.P. Ershov INSTITUTE OF INFORMATICS SYSTEMS, Russian Academy of Sciences, Siberian Branch, Novosibirsk, Russia
Polytechnic of Turin, Italy
University of Udine, Italy

Weekly seminars

Logic Seminars
Student seminars

Advanced Courses

An introduction to normal tower forcings (M. Viale)
Model Theory (D. Zambella)
An introduction to large cardinals and elementary embeddings (A. Andretta)
Assiomi di forcing e forcing iterato (M. Viale)

Workshops at the University of Torino

Young Set Theory Workshop 2013, Santuario di Oropa (Italy), 9.6.2013—14.6.2013

Research grants

Young researchers grant "Rita Levi Montalcini" 2012: "New Advances in Descriptive Set Theory"
Local Research Project — Progetti di Ricerca finanziati dall’Università di Torino (ex 60%) 2014, linea A: “Modelli e Insiemi”
Local Research Project — Progetti di Ricerca finanziati dall’Università di Torino (ex 60%) 2013, linea A: “Modelli e Insiemi"
PRIN 2012: "Logica, Modelli e Insiemi" (2012LZEBFL)
Junior PI Grant 2012 Compagnia di San Paolo: "New Perspectives On The Nature of Infinity"

Invited talks and seminars (2013-2014)

Alessandro Andretta

Le direzioni della teoria degli insiemi nel mondo e le loro ramificazioni in Italia, XXV Incontro AILA, SNS Pisa (Italia), 17.4.2014
Descriptive set theory and the density point property, Freiburg (Germany) 10.6.2014
Souslin quasi-orders and definable cardinality, First Arctic Set Theory Workshop, Kilpisjärven (Finland), 3.2.2013

Luca Motto Ros

The Hurewicz dichotomy for generalized Baire spaces, Amsterdam Workshop on Set Theory 2014, Amsterdam (Holland), 3.11.2014
Towards a descriptive set theory for computer science, INFTY Final Conference, Hausdorff Research Institute for Mathematics (HIM), University of Bonn (Germany), 4.3.2014
On the descriptive set-theoretical complexity of the embeddability relation between uncountable models, Set Theory Workshop (ID 1403), Mathematisches Forschungsinstitut Oberwolfach (Germany), 15.1.2014
Lipschitz and uniformly continuous reducibilities, Descriptive Set Theory in Paris, Institute of Mathematics of Jussieu, Pierre and Marie Curie University, Paris VI (France), 17.12.2013
Wadge-like reducibilities on arbitrary quasi-Polish spaces: a survey, Seminar “Duality in Computer Science”, Leibniz-Zentrum für Informatik, Dagstuhl (Germany), 1.8.2013
On the invariant universality property, Sy David Friedman’s 60th Birthday Conference, Kurt Gödel Research Center, Vienna (Austria), 8.7.2013
On the complexity of the embeddability relation between uncountable models, 6th Young Set Theory Workshop, Santuario di Oropa (Italy), 13.6.2013
Uniformly continuous and Lipschitz reducibilities on ultrametric Polish spaces, Oberseminar Mathematische Logik, Rheinische Friedrich-Wilhelms-Universität, Bonn (Germany), 25.11.2013
Wadge-like reducibilities on ultrametric Polish spaces, Seminarium Teoria Mnogosci (Set Theory Seminar), University of Warsaw (Poland), 15.5.2013

Matteo Viale

Iterated forcing defined by means of Boolean algebras, Winter School in Abstract Analysis — Section Set Theory and Topology, Hejnice (Czech republic), 26.1.2014—2.2.2014
Generic absoluteness versus absoluteness: a survey of recent results, SLALM 2014, Buenos Aires (Argentina), 28.7.2014—1.8.2014
Generic absoluteness for models of strong forcing axioms, North American ASL annual meeting, Waterloo (Canada), 8.5.2013—11.5.2013

2020

Raphaël Carroy, Benjamin D. Miller, Dániel T. Soukup
The open dihypergraph dichotomy and the second level of the Borel hierarchy.
https://iris.unito.it/handle/2318/1793434

Raphaël Carroy, Benjamin D. Miller
Bases for functions beyond the first Baire class.
https://iris.unito.it/handle/2318/1793429

Raphaël Carroy, Andrea Medini, Sandra Müller
Every zero-dimensional homogeneous space is strongly homogeneous under determinacy.
https://iris.unito.it/handle/2318/1736803

Raphaël Carroy, Yann Pequignot
Well, Better and In-Between.
https://iris.unito.it/handle/2318/1722705

Riccardo Camerlo, Alberto Marcone, Luca Motto Ros
Polish metric spaces with fixed distance set.
https://iris.unito.it/handle/2318/1767929

Filippo Calderoni, Heike Mildenberger, Luca Motto Ros
Uncountable structures are not classifiable up to bi-embeddability.
https://iris.unito.it/handle/2318/1714241

Saharon Shelah, Gianluca Paolini
Automorphism groups of countable stable structures.
https://iris.unito.it/handle/2318/1736593

2019

Alessandro Andretta, Riccardo Camerlo
Analytic sets of reals and the density function in the Cantor space.
https://iris.unito.it/handle/2318/1687324

Raphaël Carroy
Functions of the first Baire class.
https://iris.unito.it/handle/2318/1722701

Riccardo Camerlo, Raphaël Carroy, Alberto Marcone
Linear orders: When embeddability and epimorphism agree.
https://iris.unito.it/handle/2318/1722625

Raphaël Carroy, Yann Pequignot, Zoltán Vidnyánszky
Embeddability on functions: Order and chaos.
https://iris.unito.it/handle/2318/1722621

Gianluca Paolini, Saharon Shelah
Reconstructing structures with the strong small index property up to bi-definability.
https://iris.unito.it/handle/2318/1736592

Tapani Hyttinen, Gianluca Paolini
Coxeter groups and abstract elementary classes: The right-angled case.
https://iris.unito.it/handle/2318/1736591

Gianluca Paolini, Saharon Shelah
Polish topologies for graph products of groups.
https://iris.unito.it/handle/2318/1702553

Eugenio Colla, Domenico Zambella
Ramsey's coheirs.
https://iris.unito.it/handle/2318/1702851

2018

Alessandro Andretta
Cantor's Continuum Hypothesis: consequences in mathematics and its foundations.
https://iris.unito.it/handle/2318/1691854

Alessandro Andretta, Riccardo Camerlo, Camillo Costantini
Lebesgue density and exceptional points.
https://iris.unito.it/handle/2318/1687325

Alessandro Andretta, Vincenzo Dimonte
The iterability hierarchy above I3.
https://iris.unito.it/handle/2318/1687323

Riccardo Camerlo, Alberto Marcone, Luca Motto Ros
On isometry and isometric embeddability between ultrametric Polish spaces.
https://iris.unito.it/handle/2318/1663738

Filippo Calderoni, Luca Motto Ros
Universality of group embeddability.
https://iris.unito.it/handle/2318/1658475

Gianluca Paolini
The class of non-Desarguesian projective planes is Borel complete.
https://iris.unito.it/handle/2318/1702557

Gianluca Paolini, Saharon Shelah
The automorphism group of Hall’s universal group.
https://iris.unito.it/handle/2318/1702556

Gianluca Paolini, Saharon Shelah
Polish topologies for graph products of cyclic groups.
https://iris.unito.it/handle/2318/1702555

Tapani Hyttinen, Gianluca Paolini
Beyond abstract elementary classes: On the model theory of geometric lattices.
https://iris.unito.it/handle/2318/1702554

Matteo Viale
New axioms in set theory.
https://iris.unito.it/handle/2318/1758626

Domenico Zambella
A Crèche Course in Model Theory.
https://iris.unito.it/handle/2318/1772505

2017

Raphaël Carroy, Benjamin D. Miller
Sigma-continuity with closed witnesses.
https://iris.unito.it/handle/2318/1722703

Luca Motto Ros
Can we classify complete metric spaces up to isometry?
https://iris.unito.it/handle/2318/1632715

Gianluca Paolini, Saharon Shelah
No Uncountable Polish Group Can be a Right-Angled Artin Group.
https://iris.unito.it/handle/2318/1702561

Gianluca Paolini, Saharon Shelah
Group metrics for graph products of cyclic groups.
https://iris.unito.it/handle/2318/1702560

Tapani Hyttinen, Gianluca Paolini, Jouko Väänänen
A logic for arguing about probabilities in measure teams.
https://iris.unito.it/handle/2318/1702559

Gianluca Paolini
A Finite Axiomatization of G-Dependence.
https://iris.unito.it/handle/2318/1702558

Giorgio Audrito, Matteo Viale
Absoluteness via resurrection.
https://iris.unito.it/handle/2318/1635434

Andrea Vaccaro, Matteo Viale
Generic absoluteness and Boolean names for elements of a Polish space.
https://iris.unito.it/handle/2318/1635427

2016

Philipp Lücke, Luca Motto Ros, Philipp Schlicht
The Hurewicz dichotomy for generalized Baire spaces.
https://iris.unito.it/handle/2318/1561509

Tapani Hyttinen, Gianluca Paolini
Reduction of database independence to dividing in atomless Boolean algebras.
https://iris.unito.it/handle/2318/1702563

Gianluca Paolini, Jouko Väänänen
Dependence logic in pregeometries and ω-stable theories.
https://iris.unito.it/handle/2318/1702562

Matteo Viale
Forcing the truth of a weak form of Schanuel’s conjecture.
https://iris.unito.it/handle/2318/1635187

Matteo Viale
Martin's maximum revisited.
https://iris.unito.it/handle/2318/1558271

Matteo Viale
Category forcings, MM⁺⁺⁺, and generic absoluteness for the theory of strong forcing axioms.
https://iris.unito.it/handle/2318/1530195

Domenico Zambella
On the diameter of Lascar strong types after Ludomir Newelski.
https://iris.unito.it/handle/2318/1655603

2015

Alessandro Andretta
Direzioni della logica in Italia: la teoria degli insiemi.
https://iris.unito.it/handle/2318/1570464

Riccardo Camerlo, Raphaël Carroy, Alberto Marcone
Epimorphisms Between Linear Orders.
https://iris.unito.it/handle/2318/1554310

Luca Motto Ros, Philipp Schlicht, Victor Selivanov
Wadge-like reducibilities on arbitrary quasi-Polish spaces.
https://iris.unito.it/handle/2318/148821

Tapani Hyttinen, Gianluca Paolini, Jouko Väänänen
Quantum team logic and Bell’s inequalities.
https://iris.unito.it/handle/2318/1702566

Gianluca Paolini
Independence logic and abstract independence relations.
https://iris.unito.it/handle/2318/1702564

Domenico Zambella
Elementary classes of finite VC-dimension.
https://iris.unito.it/handle/2318/1507574

Stefano Baratella, Domenico Zambella
The Real truth.
https://iris.unito.it/handle/2318/150264

2014

Alessandro Andretta
Elementi di Logica Matematica.
https://iris.unito.it/handle/2318/151251

Raphaël Carroy, Yann Pequignot
From well to better, the space of ideal.
https://iris.unito.it/handle/2318/150245

Raphaël Carroy
Playing in the first Baire class.
https://iris.unito.it/handle/2318/150244

Luca Motto Ros, Philipp Schlicht
Lipschitz and uniformly continuous reducibilities on ultrametric Polish spaces.
https://iris.unito.it/handle/2318/148819

Luca Motto Ros
Bad Wadge-like reducibilities on the Baire space.
https://iris.unito.it/handle/2318/148781

2013

Alessandro Andretta, Riccardo Camerlo
The descriptive set theory of the Lebesgue Density Theorem.
https://iris.unito.it/handle/2318/129352

Raphaël Carroy
A quasi-order on continuous functions.
https://iris.unito.it/handle/2318/1503059

Luca Motto Ros
On the structure of finite level and omega-decomposable Borel functions.
https://iris.unito.it/handle/2318/148820

Miroslav Kačena, Luca Motto Ros, Brian Semmes
Some observations on 'A new proof of a theorem of Jayne and Rogers'.
https://iris.unito.it/handle/2318/148782

Luca Motto Ros
The descriptive set-theoretical complexity of the embeddability relation on models of large size.
https://iris.unito.it/handle/2318/148729

Riccardo Camerlo, Alberto Marcone, Luca Motto Ros
Invariantly universal analytic quasi-orders.
https://iris.unito.it/handle/2318/148726

Sean Cox, Matteo Viale
Martin’s Maximum and tower forcing.
https://iris.unito.it/handle/2318/139467

2012

Alessandro Andretta
Book review of MR2463612: Games, scales, and Suslin cardinals. The Cabal Seminar, Volume I.
https://iris.unito.it/handle/2318/130061

Alessandro Andretta, Alain Louveau
Wadge Degrees and Pointclasses.
https://iris.unito.it/handle/2318/93208

Luca Motto Ros
On the complexity of the relations of isomorphism and bi-embeddability.
https://iris.unito.it/handle/2318/148703

Matteo Viale
Guessing models and generalized Laver diamond.
https://iris.unito.it/handle/2318/97165

Silvia Barbina, Domenico Zambella
Generic expansions of countable structures.
https://iris.unito.it/handle/2318/78281

2011

Alessandro Andretta
Wadge degrees.
https://iris.unito.it/handle/2318/151505

Luca Motto Ros
Game representations of classes of piecewise definable functions.
https://iris.unito.it/handle/2318/148728

Sy-David Friedman, Luca Motto Ros
Analytic equivalence relations and bi-embeddability.
https://iris.unito.it/handle/2318/148724

Matteo Viale, Christoph Weiß
On the consistency strength of the proper forcing axiom.
https://iris.unito.it/handle/2318/97164

Domenico Zambella
Krull dimension of types in a class of first-order theories.
https://iris.unito.it/handle/2318/71614

2010

Luca Motto Ros, Brian Semmes
A new proof of a theorem of Jayne and Rogers.
https://iris.unito.it/handle/2318/148783

Luca Motto Ros
Baire reductions and good Borel reducibilities.
https://iris.unito.it/handle/2318/148731

Luca Motto Ros
Beyond Borel-amenability: scales and superamenable reducibilities.
https://iris.unito.it/handle/2318/148727

Assaf Sharon, Matteo Viale
Some consequences of reflection on the approachability ideal.
https://iris.unito.it/handle/2318/70929

Silvia Barbina, Domenico Zambella
A viewpoint on amalgamation classes.
https://iris.unito.it/handle/2318/78411

2009

Luca Motto Ros
A new characterization of Baire class 1 functions.
https://iris.unito.it/handle/2318/148784

Luca Motto Ros
Borel-Amenable Reducibilities for Sets of Reals.
https://iris.unito.it/handle/2318/148730

Matteo Viale
On the mapping reflection principle MRP.
https://iris.unito.it/handle/2318/61166

2008

Alessandro Andretta, Keith Kearnes, Domenico Zambella
Logic colloquium 2004.
https://iris.unito.it/handle/2318/60445

Matteo Viale
A family of covering properties.
https://iris.unito.it/handle/2318/58284

Matteo Viale
Forcing axioms, supercompact cardinals, singular cardinals combinatorics.
https://iris.unito.it/handle/2318/57729

2007

Alessandro Andretta, Greg Hjorth, Itay Neeman
Effective Cardinals of Boldface Pointclasses.
https://iris.unito.it/handle/2318/22825

Alessandro Andretta
The SLO Principle and the Wadge hierarchy.
https://iris.unito.it/handle/2318/5146

Silvia Barbina, Domenico Zambella
Baire categories of expansions of first-order models.
https://iris.unito.it/handle/2318/21142

2006

Alessandro Andretta
More on Wadge Determinacy.
https://iris.unito.it/handle/2318/7840

Matteo Viale
The proper forcing axiom and the singular cardinal hypothesis.
https://iris.unito.it/handle/2318/58283

2005

Alessandro Andretta, Riccardo Camerlo
The use of complexity hierarchies in descriptive set theory and automata theory.
https://iris.unito.it/handle/2318/7829

2004

Matteo Viale
The cumulative hierarchy and the constructible universe of ZFA.
https://iris.unito.it/handle/2318/58282

2003

Alessandro Andretta
Risultati di assolutezza in teoria degli insiemi (parte seconda).
https://iris.unito.it/handle/2318/7828

Alessandro Andretta
Risultati di assolutezza in teoria degli insiemi (parte prima).
https://iris.unito.it/handle/2318/7827

Alessandro Andretta, Donald A. Martin
Borel-Wadge degrees.
https://iris.unito.it/handle/2318/7826

Alessandro Andretta
Equivalence between Wadge and Lipschitz determinacy.
https://iris.unito.it/handle/2318/7825

Silvio Valentini, Matteo Viale
A binary modal logic for the intersection types of lambda-calculus.
https://iris.unito.it/handle/2318/58281

2001

Alessandro Andretta, Alberto Marcone
Pointwise convergence and the Wadge hierarchy.
https://iris.unito.it/handle/2318/7824

Alessandro Andretta, Itay Neeman, John Steel
The domestic levels of K^c are iterable.
https://iris.unito.it/handle/2318/7823

Alessandro Andretta, Alberto Marcone
Definability in function spaces.
https://iris.unito.it/handle/2318/7822

Alessandro Andretta, Riccardo Camerlo, Greg Hjorth
Conjugacy equivalence of subgroups.
https://iris.unito.it/handle/2318/7821

Alessandro Andretta, Alberto Marcone
Projective sets and ordinary differential equations.
https://iris.unito.it/handle/2318/7820

Domenico Zambella, Sebastiaan A. Terwijn
Computational randomness and lowness.
https://iris.unito.it/handle/2318/10677

Antonella Mancini, Domenico Zambella
A note on recursive models of set theories.
https://iris.unito.it/handle/2318/10676

1997

Alessandro Andretta, John Steel
How to win some simple iteration games.
https://iris.unito.it/handle/2318/7819

Alessandro Andretta, Alberto Marcone
Ordinary differential equations and descriptive set theory: uniqueness and globality of solutions of Cauchy problems in one dimension.
https://iris.unito.it/handle/2318/7818

1991

Alessandro Andretta
Large cardinals and iteration trees of height ω.
https://iris.unito.it/handle/2318/7817

Alessandro Andretta
Building iteration trees.
https://iris.unito.it/handle/2318/7816