Orateur(s)  Rahman Mohammadpour  Wien,

Titre  Specializing trees of height \omega_2 with finite approximation 
Date  10/02/2021 
Horaire  16:00 à 17:15 

Diffusion  https://uparis.zoom.us/rec/share/D1xat237ZQVoKmpuIzvHv_vMNVizFHRJMC4ExYb3pWBJDtWTZAxWVU5KpkJaKjlM.2hcMddHxDVxnXYXs 
Résume  It is wellknown that under CH one can attempt to specialize trees of height ω_2 without cofinal branches using a naive forcing with countable approximations. However, one has to require more (the nonexistence of ascending paths) than the lack of cofinal branches to make sure that the naive attempt does not fail.
I will discuss these possible obstacles to specialize trees of height ω_2 , and then
use models as side conditions to construct a forcing notion with finite conditions, which under PFA specializes a given tree of height ω_2 without cofinal branches.
If time permits, I will mention generalizations of this result to taller trees. 
Salle  Contacter Silvain Rideau ou Alessandro Vignati 
Adresse  