3 papers
math.LO2025
Aronszajn trees and maximality
Omer Ben-Neria, Siiri Kivimäki, Menachem Magidor +1
Assuming the consistency of a weakly compact cardinal above a regular uncountable cardinal , we prove the consistency of the existence of a wide -Aronszajn tree, i.e. a t…
math.LO2025
New inner models from second order logics
Menachem Magidor, Jouko Väänänen
We define a new inner model C2(omega) based on the fragment of second order logic in which second order variables range over countable subsets of the domain. We compare C2(omega) t…
math.LO2025
The tree property on long intervals of regular cardinals
James Cummings, Yair Hayut, Menachem Magidor +3
In this paper we prove that the tree property can hold on regular cardinals in an interval which overlaps a strong limit cardinal. This is a crucial milestone in the long term proj…