Aleksander Cieślak

# Aleksander Cieślak: Ideals of subsets of plane

Tuesday, October 10, 2017 17:15

Room: D1-215

Speaker:
Aleksander Cieślak

Title: Ideals of subsets of plane

Abstract. For given two ideals I and J of subsets of Polish space X we define a Fubini product $$I \times J$$ as all these subsets of plane $$X^2$$ which can be covered by a Borel set B such that I-almost all its vertical sections are J-small. We will investigate how properties of factors influence properties of product.

# Aleksander Cieślak: Cohen-stable families of subsets of integers

Tuesday, June 13, 2017 17:15

Room: D1-215

Speaker:
Aleksander Cieślak

Title: Cohen-stable families of subsets of integers

Abstract. A mad family is Cohen-stable if it remains maximal in any Cohen generic extension. Otherwise it is Cohen-stable. We will find condition necessary and sufficient for mad family to be Cohen-unstabe and investigate when such family exist.

# Aleksander Cieślak: Indescructible tower

Tuesday, April 11, 2017 17:15

Room: D1-215

Speaker:
Aleksander Cieślak

Title: Indescructible tower

Abstract. Following the Kunen's construction of m.a.d. family which is indestructible over adding $$\omega_2$$ Cohen reals we provide analogous construction for indestructibe tower.

# Aleksander Cieślak: Strongly meager sets and subsets of the plane

Tuesday, December 20, 2016 17:15

Room: D1-215

Speaker:
Aleksander Cieślak

Title: Strongly meager sets and subsets of the plane

Abstract. We will show some results proved by J. Pawlikowski in "Strongly meager sets and subsets of the plane".

# Aleksander Cieślak: Nonmeasurable images in Polish space with respect to selected sigma ideals

Tuesday, October 11, 2016 17:15

Room: D1-215

Speaker:
Aleksander Cieślak

Title: Nonmeasurable images in Polish space with respect to selected sigma ideals

Abstract. We present results on nonmeasurability (with respect to a selected σ-ideal on a Polish space) of images of functions defined on Poilish spaces. In particular, we give a positive answer to the following question: Is there a subset of the unit disc in the real plane such that continuum many projections onto lines are Lebesgue measurable and continuum many projections are not? Results were obtained together with Robert Rałowski.

# Aleksander Cieślak: Filters and sets of Vitali's type

Tuesday, February 23, 2016 17:15

Room: D1-215

Speaker:
Aleksander Cieślak

Title: Filters and sets of Vitali's type

Abstract. In construction of classical Vitali set on $$\{0,1\}^{\omega}$$ we use filter of cofinite sets to define rational numbers. We replece cofinite filter by any nonprincipal filter on $$\omega$$ and ask some  questions about measurability and cardinality of selectors and equevalence classes.

# Aleksander Cieślak: On nonmeasurable subsets of $$\mathbb{R}$$ and $$\mathbb{R}^2$$

Tuesday, October 27, 2015 17:15

Room: D1-215

Speaker:
Aleksander Cieślak

Title: On nonmeasurable subsets of $$\mathbb{R}$$ and $$\mathbb{R}^2$$

Abstract. I would like to present some results connected with the existence of a subset $$X$$ of the square $$[0,1]^2$$ with the property that for any line $$L$$ outside $$[0,1]^2$$ the projection $$\pi_L[X]$$ is completely nonmeasurable in some interval with respect to selected $$\sigma$$-ideal with Borel base on the line $$L$$.

Moreover, I will discuss the existence of large midpoint-free subsets of arbitrary subset of the real line.