The *-Prikry condition

Vincenzo Dimonte

Abstrakt

In this paper we isolate a property for forcing notions, the *-Prikry condition, that is similar to the Prikry condition but that is topological: A forcing P satis es it i for every p 2 P and for every open dense D  P, there are n 2 ! and q  p such that for any r  q with l(r) = l(q) + n, r 2 D, for some length notion l. This is implicit in many proofs in literature. We prove this for the tree Prikry forcing and the long extender Prikry forcing.

Słowa kluczowe: Prikry forcing
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