The ideal of the strongly porous sets in the real line.

Osoba referująca: 
Arturo Martinez Celis
Data spotkania seminaryjnego: 
poniedziałek, 10. Grudzień 2018 - 16:20
In the literature there are many different notions of porosity and one of them is the notion of strong porosity: Given a completely metrizable space X, a subset A of X is a strongly porous set if there is a positive constant p such that for any open ball B of radius r smaller than 1, there is an open ball B' inside of B of radius rp such that B' evades the set A. In this talk we will study the cardinal invariants of the sigma ideal generated by the strongly porous sets of the real line and the Cantor space, their relation with different notions of porosity and with other notions in set theory. In particular we will show the notion of strong porosity induces a combinatorial property on trees and we will see that these trees have a connection with the Sacks forcing and some cardinal invariants related to Martin's axiom.