Grzegorz Plebanek

# Grzegorz Plebanek: Strictly positive measures on Boolean algebras

20/03/18 21:43

Tuesday, March 27, 2018 17:15

It turns out that the positive answer follows from the existence of some large cardinals, while the counterexample can be found in the model of \(V=L\).

*Room:*D1-215*Grzegorz Plebanek*

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*Title*: Strictly positive measures on Boolean algebras*Abstract*. \(SPM\) denotes the class of Boolean algebras possessing strictly positive measure (finitely additive and probabilistic). Together with Menachem Magidor, we consider the following problem: Assume that \(B\) belongs to \(SPM\) for every subalgebra \(B\) of a given algebra \(A\) such that \(|B|\le\mathfrak c\). Does it imply that the algebra \(A\) belongs to \(SPM\)?It turns out that the positive answer follows from the existence of some large cardinals, while the counterexample can be found in the model of \(V=L\).

# Grzegorz Plebanek: On almost disjoint families with property (R)

07/03/18 21:13

Tuesday, March 13, 2018 17:15

*Room:*D1-215*Grzegorz Plebanek*

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*Title*: On almost disjoint families with property (R)*Abstract*. We consider (with A.Aviles and W. Marciszewski) almost disjoint families with some combinatorial property that has applications in functional analysis. We are looking for the minimal cardinality of m.a.d. family with property (R). It turns out that this cardinal is not greater than \(non(\mathcal{N})\) the uniformity of null sets.# Grzegorz Plebanek: About a particular measure on the square

13/12/14 03:14

Tuesday, December 16, 2014 17:15

*Room:*D1-215*Grzegorz Plebanek*

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*Title*: About a particular measure on the square*Abstract*. Assuming the existence of SierpiĆski set we construct a measure on some \(\sigma\)-field of subsets of the square which is perfect but not compact. This construction in 2001 answered Fremlin's question. We will describe open problems connected to this field.