Infinitary Proof Theory: Techniques and Applications (25w5423)


Juan Aguilera (TU Vienna)

Bahareh Afshari (University of Gothenburg)

Michael Rathjen (University of Leeds)


The Casa Matemática Oaxaca (CMO) will host the "Infinitary Proof Theory: Techniques and Applications" workshop in Oaxaca, from August 10 to August 15, 2025.

New mathematics are discovered by proving new theorems. Proofs are mathematical arguments for why a given claim must hold true. Proof Theory studies mathematical tools as mathematical objects and is concerned with the rules of mathematics, its limits, and the limits of provability; thus, we study the rules of mathematics, using mathematical tools ourselves. In Infinitary Proof Theory, one considers the possibility of extending the rules of mathematics to allow for reasoning with infinitely many steps, thus allowing us to prove mathematical results that couldn't have been proved otherwise.

The current workshop will gather world experts in the field of Infinitary Proof Theory to discuss current developments, techniques, tools, and its applications in and outside of mathematics.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF) and Alberta's Advanced Education and Technology.