Reverse Mathematics

Reverse Mathematics addresses the question of which axioms of mathematics are necessary in order to prove a specific theorem or develop a specific branch of mathematics. This often reveals new insights on these theorems and branches, such as connections with other parts of mathematics, generalizations, and explicit proofs that provide additional information on the objects constructed. The program will gather experts who have contributed to the development of the field in its first 50 years in order to discuss recent advances and future directions, as well as explore and expand its connections with other fields of mathematics.

The program will last 10 weeks and include visits from researchers, collaborations, talks, and four weeks of focus workshops. 

Week 2 (June 30–July 4). Workshop "Reverse Mathematics and Higher Computability Theory."
Higher Computability Theory (or Higher Recursion Theory) investigates generalized notion of computability, e.g., carried out over the real numbers, abstract structures, or in infinite time, as well as its connections with definability, notions of complexity, and model theory. By establishing connections with computability in the usual sense, Higher Computability Theory has deep interactions with Reverse Mathematics. This will be the topic of the workshop.

Week 6 (July 28–August 1). Summer School "Reverse Mathematics: New Paradigms."

The summer school will feature courses by the following lecturers:

Damir Dzhafarov (UConn). From topology to combinatorics, via reverse mathematics.
Ekaterina Fokina (TU Wien). Computable structure theory.
Anton Freund (U Würzburg). The strength of better-quasi-orderings, via ordinal analysis.
Ludovic Patey (Paris). Lowness and avoidance: a guide to separation.
Keita Yokoyama (Tohoku). Reverse mathematics for
analysis: an introduction

Week 7 (August 4–8). Workshop "Reverse Mathematics: New Paradigms."
The "Big Five" systems of Reverse Mathematics are commonly said to suffice for capturing the strength of "most" mathematical theorems. The New Paradigms workshop will welcome explorations into recent and future developments beyond the Big Five involving stronger axiomatic systems, weaker axiomatic systems, or "adjacent" axiomatic systems, as well as new potential approaches to Reverse Mathematics, e.g., in terms of higher-type or higher-order systems, or systems based on more languages other than arithmetic.

Week 10 (August 25–29). Workshop "Reverse Mathematics: Beyond Logic."
This workshop will welcome aspects of Reverse Mathematics which relate to other branches of mathematics such as topology, algebra and order theory, finite and infinite combinatorics, analysis, as well as connections with computer science, philosophy, physics, game theory, and more.

June 30, 2025
09:00 — 09:30
Registration & Welcome
09:30 — 10:15
Liang Yu (Nanjing U)
Digging Out Pointed Sets
10:15 — 10:45
Coffee Break
10:45 — 11:30
Sy David Friedman (U of Vienna)
Stability, Genericity and Strength
12:15 — 14:00
Lunch Break
14:45 — 15:30
15:30 — 16:00
Coffee Break
16:00 — 16:45
July 1, 2025
09:30 — 10:15
10:15 — 10:45
Coffee break
10:45 — 11:30
11:30 — 12:15
12:15 — 14:00
Lunch Break
14:00 — 14:45
15:30 — 16:00
Coffee Break
16:00 — 16:45
July 2, 2025
09:30 — 10:15
10:15 — 10:45
Coffee Break
10:45 — 11:30
11:30 — 12:15
Martina Iannella (TU Wien)
On Laver algebras and their embeddings
12:15 — 14:00
Lunch Break
14:00 — 14:45
Johanna Franklin (Hofstra university)
Failure modes for highness for isomorphism
14:45 — 15:30
15:30 — 16:00
Coffee Break
July 3, 2025
09:30 — 10:15
Miroslav Zeleny (Charles U, Prague)
On the Luzin-Novikov theorem
10:15 — 10:45
Coffee Break
10:45 — 11:30
Jan Kruschewski (TU Wien)
Analysis of HOD for Admissible Structures
11:30 — 12:15
Vassilios Gregoriades (National and Technical U of Athens)
Classical versions of effective Borel uniformizations
July 4, 2025
10:15 — 11:00
11:00 — 11:30
Coffee Break
11:30 — 12:15
Joseph Miller (U of Wisconsin-Madison)
Generic Muchnik reducibility
12:15 — 13:00
July 28, 2025
09:00 — 10:00
Prof. Ekaterina Fokina
10:00 — 10:20
Coffee Break
10:20 — 11:20
Prof. Ekaterina Fokina
11:20 — 11:40
Coffee Break
11:40 — 12:40
Prof. Damir Dzhafarov
12:40 — 14:30
Lunch Break
14:30 — 15:30
Prof. Keita Yokoyama
15:30 — 15:50
Coffee Break
15:50 — 16:50
Ludovic Levy Patey
July 29, 2025
09:00 — 10:00
Prof. Ekaterina Fokina
10:00 — 10:20
Coffee Break
10:20 — 11:20
Prof. Ekaterina Fokina
11:20 — 11:40
Coffee Break
11:40 — 12:40
Prof. Damir Dzhafarov
12:40 — 14:30
Lunch Break
14:30 — 15:30
Prof. Keita Yokoyama
15:30 — 15:50
Coffee Break
15:50 — 16:50
Ludovic Levy Patey
July 30, 2025
09:00 — 10:00
Prof. Damir Dzhafarov
10:00 — 10:20
Coffee Break
10:20 — 11:20
Prof. Keita Yokoyama
11:20 — 11:40
Coffee Break
11:40 — 12:40
Prof. Dr. Anton Freund
12:40 — 14:30
Lunch Break
14:30 — 15:30
Ludovic Levy Patey
15:30 — 15:50
Coffee Break
15:50 — 16:50
Ludovic Levy Patey
July 31, 2025
10:00 — 11:00
Prof. Damir Dzhafarov
11:00 — 11:30
Coffee Break
11:30 — 12:30
Prof. Keita Yokoyama
12:30 — 14:30
Lunch Break
14:30 — 15:30
Prof. Dr. Anton Freund
15:30 — 15:50
Coffee Break
15:50 — 16:50
Prof. Dr. Anton Freund
Aug. 1, 2025
10:00 — 11:00
Prof. Damir Dzhafarov
11:00 — 11:30
Coffee Break
11:30 — 12:30
Prof. Keita Yokoyama
12:30 — 14:30
Lunch Break
14:30 — 15:30
Prof. Dr. Anton Freund
15:30 — 15:50
Coffee Break
15:50 — 16:50
Prof. Dr. Anton Freund
This event has no subevents associated to it.

Organizers

Name Affiliation
Juan Aguilera Technical University of Vienna
Linda Brown Westrick The Pennsylvania State University
Noam Greenberg Victoria University of Wellington
Denis Hirschfeldt University of Chicago

Attendees

Name Affiliation
Miguel Aguilar TU Wien
Alessandro Andretta University of Torino
Heidi Benham University of Connecticut
Kenza Benjelloun Université Côte d'Azur
Sapir Ben-Shahar University of Wisconsin-Madison
Laurent Bienvenu Centre National de la Recherche Scientifique
Gabriele Buriola University of Verona
Lorenzo Carlucci La Sapienza University of Rome
Raphaël Carroy University of Torino
William Chan Technical University of Vienna
Peter Cholak University of Notre Dame du Lac
Alakh Dhruv Chopra Ghent University
Chris Conidis City University New York
Andrew DeLapo University of Connecticut
Andres Diaz Rojas Universitat de Barcelona, ICCUB
Isabel Diaz Rojas University of Sheffield
Natasha Dobrinen University of Notre Dame du Lac
Gavin Dooley University of Notre Dame du Lac
François Dorais University of Vermont
Damir Dzhafarov University of Connecticut
Luca Facchinetti University of Udine
Anton Fernández TU Wien
David Fernández-Duque University of Barcelona
Ekaterina Fokina TU Wien
Johanna Franklin Hofstra University
Anton Freund University of Würzburg
Sy David Friedman University of Vienna
Yuxiao Fu University of Connecticut
Elijah Gadsby City University New York
Mariami Gamsakhurdia TU Wien
Su Gao Nankai University
Giorgio Genovesi University of Leeds
Kenneth Gill La Salle University
Oriola Gjetaj Ghent University
Sarah Gleghorn University of Cambridge
Jun Le Goh National University of Singapore
David Gonzalez University of California, Berkeley
Zakkai Goriely University of California, Berkeley
Vassilios Gregoriades National and Technical University of Athens
Piotr Gruza University of Warsaw
Ellen Hammatt TU Wien
Jeffry Hirst Appalachian State University
Edward Hou Caltech University
Martina Iannella TU Wien
Corrie Ingall University of Connecticut
Josiah Jacobsen-Grocott Nanyang Technological University Singapore
Hanul Jeon Cornell University
Liling Ko TU Wien
Ulrich Kohlenbach Technical University Darmstadt
Leszek Kołodziejczyk University of Warsaw
Thibaut Kouptchinsky TU Wien
Jan Kruschewski TU Wien
Vlad Lazar Ghent University
Dominique Lecomte University Paris Jussieu
Ludovic Levy Patey CNRS Paris
Lu Liu Central South University
Robert Lubarsky Florida Atlantic University
Philipp Lücke University of Hamburg
Alberto Marcone University of Udine
Andrew Marks University of California, Berkeley
Joseph Miller University of Wisconsin-Madison
Russell Miller City University of New York
Sheila Miller Edwards Arizona State University
Antonio Montalbán University of California, Berkeley
Carl Mummert Marshall University
Antonio Nakid Cordero University of Wisconsin-Madison
Selwyn Ng Nanyang Technological University Singapore
Orazio Nicolosi University of Torino
Andre Nies University of Auckland
Gian Marco Osso University of Udine
Fedor Pakhomov Ghent University
Aristotelis Panagiotopoulos University of Vienna
Konstantinos Papafilippou Ghent University
Alvaro Pintado University of Pennsylvania
Nicholas Pischke Technical University Darmstadt
Philipp Provenzano Ghent University
Dino Rossegger TU Wien
Sam Sanders Ruhr-Universität Bochum
Philipp Schlicht University of Siena
Paul Shafer University of Leeds
Borja Sierra University of Bern
Giovanni Soldà Ghent University
Grigorii Stepanov TU Wien
Patryk Szlufik University of Warsaw
Catalina Torres University of Barcelona
Henry Towsner University of Pennsylvania
Daniel Turetsky Victoria University of Wellington
Manlio Valenti Swansea University
José Jeremías Valenzuela Morales George Washington University
Java Darleen Villano University of Connecticut
Andrea Volpi University of Udine
Wei Wang Sun Yat-sen University
Jin Wei Technical University Darmstadt
Andreas Weiermann Ghent University
Philip Welch University of Bristol
Keita Yokoyama Tohoku University
Francesca Yu University of California, Berkeley
Liang Yu Nanjing University
Miroslav Zeleny Charles University Prague
Preview of Liling Ko - Dichotomy for classes of countable graphs
Liling Ko (TU Wien): Dichotomy for classes of countable graphs
June 30, 2025 14:00 — 14:45
Preview of Liling Ko - Dichotomy for classes of countable graphs
Liling Ko (TU Wien): Dichotomy for classes of countable graphs
June 30, 2025 14:00 — 14:45
Preview of Philipp Lücke - Σ1-definability at higher cardinals
Philipp Lücke (U Hamburg): $\Sigma_1$-definability at higher cardinals
June 30, 2025 14:45 — 15:30
Preview of Raphaël Carroy - A well-quasi-order for continuous functions
Raphaël Carroy (U Torino): A well-quasi-order for continuous functions
June 30, 2025 16:00 — 16:45
Preview of Antonio Montalbán - The limit of deteremiancy in second order logic
Antonio Montalbán (UC, Berkeley): The limit of deteremiancy in second order logic
July 1, 2025 09:30 — 10:15
Preview of Dominique Lecomte (LPTHE, Paris) Strong representation of Pi03 sets and dichotomies
Dominique Lecomte (UPMC, Paris): Strong representation of Pi03 sets and dichotomies
July 1, 2025 10:45 — 11:30
Preview of Robert Lubarsky - The Reverse Mathematics of Harrington's Principle
Robert Lubarsky (FAU, Boca Ratón): The Reverse Mathematics of Harrington's Principle
July 1, 2025 11:30 — 12:15
Preview of Thibaut Kouptchinsky - The reverse mathematics of analytic measurbility
Thibaut Kouptchinsky (TU Wien): The reverse mathematics of analytic measurbility
July 1, 2025 16:00 — 16:45
Preview of Natasha Dobrinen - Computability theoretic aspects of big Ramsey degrees
Natasha Dobrinen (Notre Dame du Lac): Computability theoretic aspects of big Ramsey degrees
July 2, 2025 09:30 — 10:15
Preview of Daniel Turetsky - Iterated Graph Derivatives, Antiderivatives, and Priority Arguments
Daniel Turetsky (Victoria U of Wellington): Iterated Graph Derivatives, Antiderivatives, and Priority Arguments
July 2, 2025 10:45 — 11:30
Preview of Josiah Jacobsen-Grocott - A Weihrauch degree perspective on the difficulty of finding isomorphisms
Josiah Jacobsen-Grocott (NTU Singapore): A Weihrauch degree perspective on the difficulty of finding isomorphisms
July 2, 2025 14:45 — 15:30
At a glance
Type:
Thematic Programme
When:
June 23, 2025 — Aug. 29, 2025
Where:
ESI Schrödinger and Boltzmann Lecture Hall
Organizer(s):
Juan Aguilera (TU Vienna)
Linda Brown Westrick (Penn State U)
Noam Greenberg (Victoria U of Wellington)
Denis Hirschfeldt (U of Chicago)