5 citations · 18 across the 9 of their papers we have counts for
9 papers · 1 filter
The sharp for the Chang model is small
William Mitchell
Woodin has shown that if there is a measurable Woodin cardinal then there is, in an appropriate sense, a sharp for the Chang model. We produce, in a weaker sense, a sharp for the C…
On a Question of Hamkins and Löwe on the modal logic of collapse forcing
Mohammad Golshani, William Mitchell
Hamkins and Löwe asked whether there can be a model of set theory with the property that whenever is a generic collapse of a cardinal of onto . We giv…
One Repeat Point Gives a Closed, Unbounded Ultrafilter on {ω_1}
William J. Mitchell
It is shown that the consistency strength of ZF + DC + "the closed unbounded ultrafilter on omega_1 is an ultrafilter" is exactly ZFC + one measurable cardinal.
I[omega_2] can be the nonstationary ideal on Cof(omega_1)
William J. Mitchell
We answer a question of Shelah by showing that it is consistent that every set of ordinals of cofinality omega_1 in I[omega_2] is nonstationary if and only if it is consistent that…
Jonsson Cardinals, Erdős Cardinals, and the Core Model
William Mitchell
We show that every Jonsson cardinal is Ramsey in the Steel core model, provided that this model exists and there is no model with a Woodin cardinal. This basic result is improved i…
The covering lemma up to a Woodin cardinal
William J. Mitchell, Ernest Schimmerling, John R. Steel
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 th…