Tomasz Żuchowski

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

Tuesday, March 15, 2016 17:15

Room: D1-215

Speaker:
Tomasz Żuchowski

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

Tuesday, May 12, 2015 17:15

Room: D1-215

Speaker:
Tomasz Żuchowski

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.