## Jonathan Verner: Krom’s linearly ordered topological space which is not normal

Dear all,

The seminar meets on Wednesday 20th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Jonathan Verner will deliver a short talk on the topic announced below.
There will probably be a enough time for one more talk, volunteer
speakers are welcome.

M. Krom: A linearly ordered topological space which is not normal

Recall that in an introductory course in topology one learns that every
linearly ordered topological space is normal. If the course is good, it
is also pointed out that the construction requires the axiom of choice.
In this talk we will present a nice construction, due to Melven Krom,
which uses a specific instance of the failure of AC to build a linearly
ordered topological space which is not normal. Krom’s construction
answered an, at the time, long standing open question of Birkhoff.

Best,
David

## Jonathan Verner: Coloring metric spaces

Dear all,

The seminar meets on Wednesday December 6th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Jonathan Verner — Coloring metric spaces: A report from the oracle

“I will present a short and elegant argument, due to S. Shelah, showing how one can construct a metric space $X$ of size $2^\omega$ such that for any countable metric space  $K$ and any countable coloring of $X$ there is a monochromatic scaled copy of $K$ in $X$”.

## David Chodounsky: A generalization of the Solovay–Tennenbaum theorem

Dear all,

The seminar meets on Wednesday November 29th at 11:00 in the Institute of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
David Chodounsky will present a generalization of the Solovay–Tennenbaum theorem; Assuming a diamond principle and given a suitable class PHI of ccc posets, there is a poset in the class PHI which forces MA(PHI) and c=kappa.

## Šárka Stejskalová: Prikry-type forcings

Dear all,

The seminar meets on Wednesday November 15th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Šárka Stejskalová — Prikry-type forcings

Best,
David

## Boriša Kuzeljević: Some applications of PID

Dear all,

The seminar meets on Wednesday November 8th at 11:00.

Program: Boriša Kuzeljević — Some applications of PID
The talk will be a continuation of the talk from the previous Wednesday.

Best,
David

## Egbert Thümmel and Boriša Kuzeljević: the P-ideal dichotomy

Dear all,

The seminar meets on Wednesday November 1st at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Egbert Thümmel and Boriša Kuzeljević will review some classical
as well as new facts and applications of the P-ideal dichotomy (PID).

Best,
David

## Jan Grebik: Borel selectors of Borel ideals (continued)

Dear all,

The seminar meets on Wednesday October 25th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jan Grebik — Borel selectors of Borel ideals (continued)
We present a result that there is an F_sigma ideal without Borel
selector and deduce that Galvin’s lemma does not have a “Borel proof.”
We also show that Nash-Williams theorem has a “Borel proof” and
therefore Galvin’s lemma is intrinsically more complex than
Nash-Williams theorem.

Best,
David

## Jan Grebik: Borel selectors of Borel ideals

Dear all,

The seminar meets on Wednesday October 18th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Jan Grebik — Borel selectors of Borel ideals
We present a result that there is an F_sigma ideal without Borel
selector and deduce that Galvin’s lemma does not have a “Borel proof.”
We also show that Nash-Williams theorem has a “Borel proof” and
therefore Galvin’s lemma is intrinsically more complex than
Nash-Williams theorem.

Best,
David

## Saeed Ghasemi: Isomorphisms between reduced

Dear all,

The seminar meets on Wednesday October 11th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program: Saeed Ghasemi — Isomorphisms between reduced
products of matrices

The talk will be mostly based on the paper:
https://arxiv.org/abs/1310.1353

Best,
David

## Boriša Kuzeljević: P-ideal dichotomy and the strong form of the Souslin hypothesis

Dear all,

The seminar meets on Wednesday October 4th at 11:00 in the Institute of
Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Boriša Kuzeljević — P-ideal dichotomy and the strong form of the
Souslin hypothesis

Best,
David