On the 21th of March 2019, at 10:15 a.m.
Leszek
Ko³odziejczyk (MIMUW)
will give a talk on
"Reverse
Mathematics"
Abstract
By
Gödel's
incompleteness theorem, for any
reasonable (and
reasonably strong) theory there
exists an
undecidable sentence, i.e. a
statement in the
language of the theory which the
theory can
neither prove nor disprove. Gödel's
undecidable
sentences concerned logical
phenomena such as
provability and consistency, but it
gradually
became clear that undecidability
applies
also to statements with a more
evident
mathematical meaning.
For typical theories that attempt to
axiomatize "all of mathematics",
such as Zermelo-Fraenkel set theory,
known undecidable statements tend to
concern matters rather distant from
the everyday experience of most
mathematicians: the continuum
hypothesis, the existence of very
large cardinal numbers, and so on.
Eventually logicians began to ask
what sort of axioms are needed to
prove basic theorems about more
mundane mathematical objects such as
e.g. natural and real numbers,
continuous functions or separable
metric spaces. I will talk about a
research programme known as reverse
mathematics, which was initiated
almost 50 years in an attempt to
answer such questions.
The seminar takes place on Thursdays from 10:15 a.m. to
12:00 in the room 2.23 of the main building of the
Faculty of Physics (the 2nd floor), Pasteur Str. 5,
Warszawa.
Additional information can be found on the webpage http://oldwww.fuw.edu.pl/KMMF/sem.czw.przedp.html.
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