Fwd: Mini-course Friedrich Wehrung - May 20 - 24

Fwd: Mini-course Friedrich Wehrung - May 20 - 24

[Axel Osmond]

***Forwarding - Sorry for multiple messages ***

Dear all,

I am writing to let you know that, in the scope of the /DuaLL/ project,
*Friedrich Wehrung* is coming to Nice to give a mini-course on
"Constructing (counter)examples via condensates", in the week *May 20 -
24* (you can find the abstract below). [I apologize to those who are
receiving this e-mail twice]

Here is the planned schedule:

Mon 20: 15h -> 16h
Tue 21: 15h -> 16h
Wed 22: 15h -> 16h
Thu 23: 11h -> 12h
Fri 24: 11h -> 12h

For logistic reasons (and a request from the speaker), please let me
know by the ***May 10*** whether you'll be attending this course. In
case you wish to attend but the schedule doesn't suit you, please let me
know as soon as possible.


You can also see the following website for next planned meetings of /DuaLL/:

https://math.unice.fr/~cborlido/GdT.html

Please don't hesitate to let me know if you wish to be added to our
mailing list.

Best regards,
C??lia

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*Abstract:*

For categories A and B, the determination of the range of a given
functor F: A\to B gives often
rise to seemingly intractable problems, even at the most basic level ???
that is, does every object
of B belong to the range of F (up to isomorphism of course)? Similar,
apparently stronger questions
can be stated for arrows in B, or, more generally, for commutative
diagrams in B. It turns out that
due to a 2011 construction of the author with Pierre Gillibert, that we
called the condensate
construction, all those questions are, under fairly general conditions,
equivalent. For instance,
representing an arrow is ?? not really ?? harder than representing an
object. However, this
equivalence comes with a cost: going from a diagram counterexample to an
object counterexample
(outside the range of F) requires a cardinality jump, the amplitude of
which depends of a natural
number called the Kuratowski index (often equal to the order-dimension)
of the shape of the diagram
in question.

Recent improvements of the condensate construction made it possible to
prove stronger negative
results, stating that the range of the functor F is not even closed
under elementary equivalence
with respect to infinitary languages of the form L_{\infty,\lambda}.
Such negative results are
inferred from the existence of a (necessarily non-commutative) diagram D
in A such that F(D) is not
F(X) for any commutative diagram X in A. For example, the long-standing
problem of the
characterization of the spectra of all Abelian lattice-ordered groups
finds there a negative
solution: namely, the class of all Stone duals of such spectra (which
are special kinds of
distributive lattices with zero) is not closed under
L_{\infty,\lambda}-elementary equivalence for
any infinite cardinal \lambda; in particular, it is not the class of all
models of any class of
L_{\infty,\lambda} sentences.


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