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# CfA: SotFoM 4: Reverse Mathematics (9-11 October, LMU Munich)

01.08.2017

Reverse mathematics is concerned with examining exactly which axioms are necessary for various central mathematical theorems and results. The program is a relatively new one in the foundations of mathematics. Its basic goal is to assess the relative logical strengths of theorems from ordinary (non-set-theoretic) mathematics. To this end, for a given mathematical theorem T, one tries to find the minimal natural axiom system that is capable of proving T. In logical terms, finding the minimal axiom system equates to finding a collections of axioms such that each axiom follows from T (assuming a weak base system of axioms). In doing so, one shows that each axiom is necessary for T to hold. Because, by hypothesis, T follows from the axioms as well, the goal of reverse mathematics is to find axiom systems to which the theorems of ordinary mathematics are equivalent. It turns out that most theorems are equivalent to one of five subsystems of second order arithmetic.

The main objective of the conference is to explore the philosophical significance of reverse mathematics as a research program in the foundations of mathematics. The event will provide a forum for experts and early career researchers to exchange ideas and develop connections between philosophical and mathematical research in reverse mathematics. Specifically, the following research questions will be addressed:

1. How are philosophical debates informed by divisions between the relevant five subsystems of second order arithmetic, e.g., the debate between predicativism and impredicativism?
2. How should we understand the divisions between these five systems in terms of any natural distinctions they map on to?
3. How exhaustive are these five systems, especially in the sense of how they map onto natural divisions?
4. How does reverse mathematics relate to and inform our understanding of more traditional foundations of mathematics like ZFC, e.g., concerning the existence of large cardinals?

## Confirmed Speakers:

• Marianna Antonutti Marfori (Munich Center for Mathematical Philosophy, LMU Munich)
• Walter Dean (University of Warwick)
• Benedict Eastaugh (University of Bristol)
• Marcia Groszek (Dartmouth College)
• Takako Nemoto (Japan Advanced Institute of Science and Technology)
• Stephen G. Simpson (Pennsylvania State University and Vanderbilt University)

## Call for Abstracts:

We invite the submission of abstracts, suitable for a 40 minute talk, on topics related to any aspects of reverse mathematics. We encourage submissions from early-career researchers and PhD students. Please send an abstract of around 1000-1500 words by email to sotfom@gmail.com in PDF format. Abstracts should be prepared for blind review. The author’s name, paper title, institutional affiliation, and contact details should be included in the email.