<![CDATA[WUJ]]><![CDATA[info@ejournals.eu]]>https://www.ejournals.eu/20201020ejournals.eu.article.1229003010610.4467/20842589RM.18.007.884020<![CDATA[Prikry forcing]]>00ED031001Number10102<![CDATA[Reports on Mathematical Logic]]>03<![CDATA[2018]]>01<![CDATA[Number 53]]>1A01<![CDATA[Vincenzo Dimonte]]>0101<![CDATA[The *-Prikry condition]]>01en003103020PLN03<![CDATA[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.
Received 16 October 2017
Revised 2 June 2018
AMS subject classifications: 03E55, 03E05, 03E35(03E45)]]>012018090615000401http://dx.doi.org/10.4467/20842589RM.18.007.8840