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PRODID:ILLC Website
BEGIN:VEVENT
UID:/NewsandEvents/Events/Upcoming-Events/newsitem
/6874/22-May-2015-Cool-Logic-Hugo-Nobrega
DTSTAMP:20150518T000000
SUMMARY:Cool Logic, Hugo Nobrega
ATTENDEE;ROLE=Speaker:Hugo Nobrega
DTSTART:20150522T180000
DTEND:20150522T190000
LOCATION:ILLC Seminar Room (F1.15), Science Park 1
07, Amsterdam
DESCRIPTION:Descriptive set theory (DST) is the st
udy of the definable sets of real numbers and simi
lar topological spaces. One of DST's main driving
questions is: What can we say about a set if all t
hat we know is that it is definable with a certain
complexity? For example, we know that if a set is
the projection of a closed subset of the real pla
ne then it cannot be a counterexample to the Conti
nuum Hypothesis. On the other hand, the usual axio
ms of set theory don't determine whether the same
can be said of all *complements* of such sets! On
e especially interesting space studied in DST is t
he Baire space, composed of the infinite sequences
of natural numbers. The topology of this space ha
s a certain computational-combinatorial flavor whi
ch makes many arguments more intuitive than in oth
er spaces. Another nice aspect of this space is th
at it lends itself quite naturally to analysis by
infinite games, which I hope to convince you of in
this talk. I will start with a brief descriptio
n of some games which have far-reaching consequenc
es for set theory and the foundation of mathematic
s. The main focus of the talk will be the games wh
ich characterize interesting classes of functions
in Baire space, where I will describe results by W
adge, Duparc, Andretta, Semmes, and (time permitti
ng) yours truly. I will assume no prior knowledge
other than some basic mathematics, such as the def
inition of a topology. For more information, see
http://www.illc.uva.nl/coollogic/ or contact cooll
ogic.uva at gmail.com
X-ALT-DESC;FMTTYPE=text/html:\n Descript
ive set theory (DST) is the study of the definable
sets of real numbers and similar topological spac
es. One of DST's main driving questions is: What c
an we say about a set if all that we know is that
it is definable with a certain complexity? For exa
mple, we know that if a set is the projection of a
closed subset of the real plane then it cannot be
a counterexample to the Continuum Hypothesis. On
the other hand, the usual axioms of set theory don
't determine whether the same can be said of all *
complements* of such sets!

\n One espec
ially interesting space studied in DST is the Bair
e space, composed of the infinite sequences of nat
ural numbers. The topology of this space has a cer
tain computational-combinatorial flavor which make
s many arguments more intuitive than in other spac
es. Another nice aspect of this space is that it l
ends itself quite naturally to analysis by infinit
e games, which I hope to convince you of in this t
alk.

\n I will start with a brief desc
ription of some games which have far-reaching cons
equences for set theory and the foundation of math
ematics. The main focus of the talk will be the ga
mes which characterize interesting classes of func
tions in Baire space, where I will describe result
s by Wadge, Duparc, Andretta, Semmes, and (time pe
rmitting) yours truly. I will assume no prior know
ledge other than some basic mathematics, such as t
he definition of a topology.

\n \n For more information, see http://www.il
lc.uva.nl/coollogic/ or contact coollogic.uva at gmail.
com

\n
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/6874/22-May-2015-Cool-Logic-Hugo-Nobrega
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