[Settfa] CANCELLED: Tuesday 25 Mar, Dragan Mašulović

[David Bradley-Williams]

Dear all,

Unfortunately our planned speaker Dragan Mašulović has been unable to 
travel to Prague for his visit this week, so the seminar tomorrow is 
cancelled and we look forward to his visit sometime in the future.

Next week we plan to have a talk by Michal Doucha.

Best wishes,
David

On 2025-03-22 09:00, kubis at math.cas.cz wrote:
> Tuesday, 25 March 2025 - 10:00 to 11:30
> Place: IM, konírna
> 
>  Speaker: Dragan Mašulović, University of Novi Sad
> Title: Big Ramsey combinatorics of the Cantor set and a simple proof
> of the Blass perfect set theorem
> 
>  Abstract
> The Blass perfect set theorem states that for every positive integer
> n, every perfect set P of the reals and every finite Borel coloring of
> n-tuples of elements of P there is a perfect set Q contained in P such
> that n-tuples of Q attain at most (n - 1)! colors. In essence, this is
> a statement about the Cantor set having finite big Ramsey degrees.
> 
>  The original 1981 proof which relies on the Halpern-Läuchli theorem
> was later simplified by Todorčević who used Miliken spaces to obtain
> the same result. In this talk we will outline a much simpler proof of
> the Blass perfect set theorem based on the Carlson-Simpson theorem. We
> show that for every positive integer n there is a positive integer t
> such that for every finite Borel coloring of n-tuples of the Cantor
> set C there is a Cantor set C' contained in C such that n-tuples of C'
> attain at most t colors. The price we have to pay for the simpler
> proof is the fact that using less elaborate strategies we are no
> longer able to show that t = (n - 1)!.
> 
>  We conclude the talk with a few remarks showing that several
> structures related to the Cantor set also have finite big Ramsey
> degrees.
> 
>  For more information see the seminar web page at
> https://www.math.cas.cz/index.php/events/seminar/6
> 
>  Set Theory and Analysis mailing list
> settfa at math.cas.cz
> https://list.math.cas.cz/listinfo/settfa@math.cas.cz
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-- 
David Bradley-Williams PhD
Department of Abstract Analysis
Institute of Mathematics, Czech Academy of Sciences
Žitná 25
115 67 Praha 1
Czech Republic

Tel: +420-222 090 743

Url: http://davidbw.sdf.org/