James Cummings, Ernest Schimmerling
Abstract. We study some combinatorial principles intermediate between square and weak square. We construct models which distinguish various square principles, and show that a strengthened form of...
James Cummings, Ernest Schimmerling
. We study some combinatorial principles intermediate between square and weak square. We construct models which distinguish various square principles, and show that a strengthened form of weak square...
A Question about Suslin Trees and the Weak Square Hierarchy (2005)
We present a question about Suslin trees and the weak square hierarchy which was contributed to the list of open problems of the BIRS workshop.
Ernest Schimmerling, Boban Velickovic
We define what it means for a function on ω1 to be a collapsing function for λ and show that if there exists a collapsing function for (2 ω1 +) , then there is no precipitous ideal on ω1. We show...
c○2002 American Mathematical Society (2002)
Abstract. Theorem 4 is a characterization of Woodin cardinals in terms of Skolem hulls and Mostowski collapses. We define weakly hyper-Woodin cardinals and hyper-Woodin cardinals. Theorem 5 is a...
Ernest Schimmerling, Martin Zeman
We present a general construction of a �κ-sequence in Jensen’s fine structural extender models. This construction yields a local definition of a canonical �κ-sequence as well as a...
Square-kappa-finite, the finite family version of weak square, holds at all cardinals kappa in the Mitchell-Steel inner models.
The maximality of the core model (1997)
Schimmerling, Ernest, Steel, John R.
If T is an iteration tree on K and F is a countably certified extender that coheres with the final model of T, then F is on the extender sequence of the final model of T. Several applications of...
The covering lemma up to a Woodin cardinal (1997)
Mitchell, William J., Schimmerling, Ernest, Steel, John R.
A cardinal kappa is countably closed if mu^omega < kappa whenever mu < kappa. Assume that there is no inner model with a Woodin cardinal and that every set has a sharp. Let K be the core model....
The Jensen covering property (1997)
Schimmerling, Ernest, Woodin, W. Hugh
An optimal extension of the Jensen covering lemma, within the limits imposed by Prikry forcing, is proved. If L[E] is an "iterable" weasel with no measurable cardinals, then either L[E] has...
ANNALS OF PURE AND APPLIED LOGIC (1992)
Combinatorial principles in the core model for one Woodin cardinal