Algebra Seminar talk
2026-10-16
Tatsuya Goto
Weak notions of minimality
Abstract:
In forcing, minimality means that every new real in the extension can recover all the reals in the extension. Sacks forcing, Laver forcing, and Miller forcing have this property. We introduce the notions of d-minimality and b-minimality, which weaken minimality from the viewpoint of eventual domination of sequences. Our results are that Mathias forcing yields a d-minimal extension and that Hechler forcing yields a b-minimal extension. This is joint work with Martin Goldstern.