Logic Seminar
Ralf Schindler
Muenster
Martin's Maximum$^{++}$ implies the $P_\text{max}$ axiom $(\ast)$.
Abstract: Forcing axioms spell out the dictum that if a statement can be forced, then it is already true.
The $P_\text{max}$ axiom $(\ast)$ goes beyond that by claiming that if a statement is consistent, then it is already true.
Here, the statement in question needs to come from a restricted class of statements, and "consistent" needs to mean "consistent in a strong sense."
It turns out that $(\ast)$ is actually equivalent to a forcing axiom, and the proof is by showing that the (strong) consistency of certain theories gives rise to a corresponding notion of forcing producing a model of that theory.
This is joint work with D. Asperó building upon earlier work of R. Jensen and (ultimately) Keisler's "consistency properties."
This meeting will be using Zoom - please write an email to fcaldero@uic.edu or sinapova@uic.ed for login information.
Tuesday September 15, 2020 at 11:00 AM in Zoom