Canonical Seeds and Prikry Trees
Hamkins, Joel David
J. Symbolic Logic, Tome 62 (1997) no. 1, p. 373-396 / Harvested from Project Euclid
Applying the seed concept to Prikry tree forcing $\mathbb{P}_\mu$, I investigate how well $\mathbb{P}_\mu$ preserves the maximality property of ordinary Prikry forcing and prove that $\mathbb{P}_\mu$ Prikry sequences are maximal exactly when $\mu$ admits no non-canonical seeds via a finite iteration. In particular, I conclude that if $\mu$ is a strongly normal supercompactness measure, then $\mathbb{P}_\mu$ Prikry sequences are maximal, thereby proving, for a large class of measures, a conjecture of W. Hugh Woodin's.
Publié le : 1997-06-14
Classification: 
@article{1183745234,
     author = {Hamkins, Joel David},
     title = {Canonical Seeds and Prikry Trees},
     journal = {J. Symbolic Logic},
     volume = {62},
     number = {1},
     year = {1997},
     pages = { 373-396},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1183745234}
}
Hamkins, Joel David. Canonical Seeds and Prikry Trees. J. Symbolic Logic, Tome 62 (1997) no. 1, pp.  373-396. http://gdmltest.u-ga.fr/item/1183745234/