6 papers · 1 filter
Bar-recursion and Preservation of Cardinals
Laura Fontanella, Jacopo Furlan
This work presents a transfinite version of the bar-recursion in the context of classical realizability models for set theory. Bar-recursion has been previously used to obtain real…
Square and Delta reflection
Laura Fontanella, Yair Hayut
Starting from infinitely many supercompact cardinals, we force a model of ZFC where satisfies simultaneously a strong principle of reflection, called -reflectio…
Strong Tree Properties at Successors of Singular Cardinals
Laura Fontanella
We prove that successors of singular limits of strongly compact cardinals have the strong tree property. We also prove that aleph_{omega+1} can consistently satisfy the strong tree…
Strong Tree Properties for Small Cardinals
Laura Fontanella
An inaccessible cardinal kappa is supercompact when (kappa, lambda)-ITP holds for all lambda greater than or equal to kappa. We prove that if there is a model of ZFC with infinitel…
Oscillations and their applications in partition calculus
Laura Fontanella, Boban Velickovic
Oscillations are a powerful tool for building examples of colorings witnessing negative partition relations. We survey several results illustrating the general technique and presen…
Strong tree Properties for two successive cardinals
Laura Fontanella
An inaccessible cardinal is supercompact when -ITP holds for all We prove that if there is a model of $\ZFC$ with two supercompact cardinals, then there is a…