# [FOM] Final CFA - SotFoM4: Reverse Mathematics, Munich, 9-11 October 2017

John Wigglesworth jmwigglesworth at gmail.com
Fri Aug 4 10:50:38 EDT 2017

```Final CFA - SotFoM4: Reverse Mathematics

9 - 11 October 2017, Munich Center for Mathematical Philosophy, LMU Munich

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 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?

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 at 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 body of the email.

Notification of acceptance: 15 August 2017
Conference: 9 - 11 October, 2017

For further details on the conference, please visit:
http://sotfom.wordpress.com

Organisers:

Carolin Antos-Kuby (University of Konstanz), Neil Barton (Kurt Gödel
Research Center, Vienna), Lavinia Picollo (Munich Center for Mathematical
Philosophy), Claudio Ternullo (Kurt Gödel Research Center, Vienna), John
Wigglesworth (University of Vienna)

Thanks:

SotFoM4: Reverse Mathematics is generously supported by the Munich Center
for Mathematical Philosophy, LMU Munich, and the Deutsche
Forschungsgemeinschaft.
--
John Wigglesworth
University of Vienna
www.wigglesworth.org
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