# Miha Habič: The grounded Martin’s axiom

Dear all,

The seminar meets on Wednesday September 13th at 11:00 in the Institute
of Mathematics CAS, Zitna 25, seminar room, 3rd floor, front building.

Program:
Miha Habič — The grounded Martin’s axiom

We will examine the notion of a grounded forcing axiom, which asserts
that the universe is a forcing extension by a forcing notion from a
particular class and that the usual forcing axiom holds for forcings
from that class coming from the ground model of the extension. We shall
focus in particular on the grounded Martin’s axiom, where the universe
is a ccc extension. The principle has some of the combinatorial strength
of MA, but allows for more flexibility (for example, a singular
continuum). Furthermore, it is more robust under mild forcing extensions
than full MA, since it is often preserved after adding a Cohen or a
random real. We will also briefly glance at grounded versions of other
forcing axioms, such as grounded PFA, and outline some open questions in
the area.

Best,
David