%0 Journal Article
%T The *-Prikry condition
%A Dimonte, Vincenzo
%J Reports on Mathematical Logic
%V 2018
%R 10.4467/20842589RM.18.007.8840
%N Number 53
%P 111-142
%K Prikry forcing
%@ 0137-2904
%D 2018
%U https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/the-prikry-condition
%X 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 satisfies it iff for every p ∈Pand for every open dense D ⊆P, there are n ∈ωand q ≤∗p such that for any r ≤q with l(r) = l(q) + n, r ∈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.