Tomasz Żuchowski

# Tomasz Żuchowski: Nonseparable growth of omega supporting a strictly positive measure

14/03/16 18:57

Tuesday, March 15, 2016 17:15

Our remainder is a Stone space of a Boolean subalgebra of Lebesgue measurable subsets of \(2^{\omega}\) containing all clopen sets.

*Room:*D1-215*Tomasz Żuchowski*

Speaker:Speaker:

*Title*: Nonseparable growth of omega supporting a strictly positive measure*Abstract*. We will construct in ZFC a compactification \(\gamma\omega\) of \(\omega\) such that its remainder \(\gamma\omega\backslash\omega\) is not separable and carries a strictly positive measure, i.e. measure positive on nonempty open subsets. Moreover, the measure on our space is defined by the asymptotic density of subsets of \(\omega\).Our remainder is a Stone space of a Boolean subalgebra of Lebesgue measurable subsets of \(2^{\omega}\) containing all clopen sets.

# Tomasz Żuchowski: Tukey types of orthogonal ideals

08/05/15 08:24

Tuesday, May 12, 2015 17:15

*Room:*D1-215*Tomasz Żuchowski*

Speaker:Speaker:

*Title*: Tukey types of orthogonal ideals*Abstract*. A partial order \(P\) is Tukey reducible to partial order \(Q\) when there exists a function \(f:P\to Q\) such that if \(A\) is a bounded subset of \(Q\) then \(f^{-1}[A]\) is a bounded subset of \(P\). The existence of such reduction is related to some cardinal invariants of considered orders. We will show Tukey reductions between some special ideals of subsets of \(\mathbb{N}\) with the inclusion order and other partial orders.