TY - JOUR
TI - The *-Prikry condition
AU - Dimonte, Vincenzo
TI - The *-Prikry condition
AB - 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.
VL - 2018
IS - Number 53
PY - 2018
SN - 0137-2904
C1 - 2084-2589
SP - 111
EP - 142
DO - 10.4467/20842589RM.18.007.8840
UR - https://ejournals.eu/en/journal/reports-on-mathematical-logic/article/the-prikry-condition
KW - Prikry forcing