More forcing notions imply diamond

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Archive for Mathematical Logic 35 (5-6):299-313 (1996)
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Abstract

We prove that the Sacks forcing collapses the continuum onto ${\frak d}$ , answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses $\omega_2$ then it forces $\diamondsuit_{\omega_{1}}$

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10.1007/s001530050047

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Citations of this work

Antichains of perfect and splitting trees.Paul Hein & Otmar Spinas - 2020 - Archive for Mathematical Logic 59 (3-4):367-388.
Silver antichains.Otmar Spinas & Marek Wyszkowski - 2015 - Journal of Symbolic Logic 80 (2):503-519.
Collapsing $$omega _2$$ with semi-proper forcing.Stevo Todorcevic - 2018 - Archive for Mathematical Logic 57 (1-2):185-194.

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Set Theory.T. Jech - 2005 - Bulletin of Symbolic Logic 11 (2):243-245.
Iterated perfect-set forcing.James E. Baumgartner & Richard Laver - 1979 - Annals of Mathematical Logic 17 (3):271-288.

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