[FOM] CFR - SotFoM4: Reverse Mathematics, Munich, 9-11 October 2017

[John Wigglesworth]

CFR - 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?


Program:

Day 1 - Monday, October 9, 2017, LMU Main Building, room A 022

10:00-10:15 Welcome
10:15-11:45 Stephen G. Simpson `Foundations of mathematics: an optimistic
message’
11:45-12:15 Coffee break
12:15-13:15 Sam Sanders `Two is enough for chaos in reverse mathematics’
13:15-15:00 Lunch break
15:00-16:00 Michał Tomasz Godziszewski `What do we need to prove that
satisfaction is not absolute? Generalization of the Nonabsoluteness of
Satisfaction Theorem’
16:00-16:30 Coffee break
16:30-18:00 Walter Dean `Basis theorems and mathematical knowledge de re
and de dicto’
19:00 Conference dinner


Day 2 - Tuesday, October 10, 2017, Main Building, room E 006

10:15-11:45 Benedict Eastaugh `On the significance of reverse mathematics’
11:45-12:15 Coffee break
12:15-13:15 Marta Fiori Carones `Interval graphs and reverse mathematics’
13:15-15:00 Lunch break
15:00-16:00 Eric P. Astor `Divisions in the reverse math zoo, and the
weakness of typicality’
16:00-16:30 Coffee break
16:30-18:00 Marianna Antonutti Marfori `De re and de dicto knowledge in
mathematics: some case studies from reverse mathematics’


Day 3 - Wednesday, October 11, 2017, LMU Main Building, room A 022

10:15-11:45 Takako Nemoto `Constructive reverse mathematics and WKL’
11:45-12:15 Coffee break
12:15-13:15 Vasco Brattka `Weihrauch complexity: Choice as a unifying
principle’
13:15-15:00 Lunch break
15:00-16:00 Alberto Marcone `Around ATR_0 in the Weihrauch lattice’
16:00-16:30 Coffee break
16:30-18:00 Marcia Groszek `Reverse recursion theory’


Call for Registration:

To register for the conference, please email your name and affiliation to
sotfom at gmail.com.  There will be a conference dinner on Monday, October 9,
2017. When registering, please indicate if you plan to attend the dinner.

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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