[bibtex key=Hamkins97:Seeds]

Applying the seed concept to Prikry tree forcing ℙ𝜇, I investigate how well ℙ𝜇 preserves the maximality property of ordinary Prikry forcing and prove that ℙ𝜇 Prikry sequences are maximal exactly when 𝜇 admits no non-canonical seeds via a finite iteration.  In particular, I conclude that if 𝜇 is a strongly normal supercompactness measure, then ℙ𝜇 Prikry sequences are maximal, thereby proving, for a large class of measures, a conjecture of W. H. Woodin’s.