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More on trees and Cohen reals, part 2

Giorgio Laguzzi

Mittwoch, 15. Januar 2020 16:30Uhr

The talk is a continuation of the topic developed by Brendan Stuber-Rousselle during the previous Oberseminar, and it is based on our joint work. I will go into more details showing how the presence of a Cohen real affects the nature of the ideals of P-nowhere dense and P-meager sets, and I will sketch out a proof of the general theorem stating that when a tree-forcing P adds Cohen reals under certain reasonable assumption and F is a well-sorted family of subsets of reals, then P-measurability for all sets in F implies the Baire property for all sets in F. If there will be any time left, I will also provide more details about some basic properties of the variant of Mathias forcing introduced in our paper.