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 satisfies it iff for every p ∈Pand for every open dense D ⊆P, there are n ∈ωand q ≤∗p such that for any rq with l(r) = l(q) + n, rD, 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.

 

Received 16 October 2017

Revised 2 June 2018

AMS subject classifications: 03E55, 03E05, 03E35(03E45)

Słowa kluczowe: Prikry forcing
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