• J. D. Hamkins, “Canonical seeds and Prikry trees,” Journal of Symbolic Logic, vol. 62, iss. 2, p. 373–396, 1997.
  [Bibtex]

  @article {Hamkins97:Seeds,
  AUTHOR = {Hamkins, Joel David},
  TITLE = {Canonical seeds and {P}rikry trees},
  JOURNAL = {Journal of Symbolic Logic},
  FJOURNAL = {The Journal of Symbolic Logic},
  VOLUME = {62},
  YEAR = {1997},
  NUMBER = {2},
  PAGES = {373--396},
  ISSN = {0022-4812},
  CODEN = {JSYLA6},
  MRCLASS = {03E40 (03E05 03E55)},
  MRNUMBER = {1464105 (98i:03070)},
  MRREVIEWER = {Douglas R.~Burke},
  DOI = {10.2307/2275538},
  URL = {http://jdh.hamkins.org/seeds},
  }

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. H. Woodin’s.