Yair Hayut

On the consistency of local and global versions of Chang’s Conjecture

We show that for many pairs of infinite cardinals

ON FOREMAN’S MAXIMALITY PRINCIPLE

\kappa > \mu^+ > \mu

Restrictions on forcings that change cofinalities

,

Square and Delta reflection

(\kappa^{+}, \kappa)\twoheadrightarrow (\mu^+, \mu)

Magidor–Malitz reflection

is consistent relative to the consistency of a supercompact cardinal. We also show that it is consistent, relative to a huge cardinal that

The strong tree property and weak square

(\kappa^{+}, \kappa)\twoheadrightarrow (\mu^+, \mu)

On the verge of inconsistency: Magidor cardinals and Magidor filters

for every successor cardinal

Special Aronszajn Tree Property

\kappa

Weak prediction principles

and every

Destructibility of the tree property at

\mu < \kappa