- 12 March 2009
- journal article
- Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic
- Vol. 74 (1) , 315-335
Abstract
We show that either of the following hypotheses imply that there is an inner model with a proper class of strong cardinals and a proper class of Woodin cardinals. 1) There is a countably closed cardinal κ ≥ ℵ such that □κ and □(κ) fail. 2) There is a cardinal κ such that κ is weakly compact in the generic extension by Col(κ, κ+). Of special interest is 1) with κ = ℵ3 since it follows from PFA by theorems of Todorcevic and Velickovic. Our main new technical result, which is due to the first author, is a weak covering theorem for the model obtained by stacking mice over Kc∥κ.Keywords
This publication has 10 references indexed in Scilit:
- Coherent sequences and threadsAdvances in Mathematics, 2007
- CHARACTERIZATION OF □κ IN CORE MODELSJournal of Mathematical Logic, 2004
- Inner Models and Large Cardinals2002
- The domestic levels ofK c are iterableIsrael Journal of Mathematics, 2001
- The maximality of the core modelTransactions of the American Mathematical Society, 1999
- The Core Model Iterability Problem1996
- Combinatorial principles in the core model for one Woodin cardinalAnnals of Pure and Applied Logic, 1995
- Fine Structure and Iteration Trees1994
- Forcing axioms and stationary setsAdvances in Mathematics, 1992
- A note on the proper forcing axiom1984