More forcing notions imply diamond

Andrzej Rosłanowski; Saharon Shelah

doi:10.1007/s001530050047

More forcing notions imply diamond

Andrzej Rosłanowski^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We prove that the Sacks forcing collapses the continuum onto δ, answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses ω ₂ then it forces ◇ _ω1 .

Original language	English
Pages (from-to)	299-313
Number of pages	15
Journal	Archive for Mathematical Logic
Volume	35
Issue number	5-6
DOIs	https://doi.org/10.1007/s001530050047
State	Published - Nov 1996

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abstract = " We prove that the Sacks forcing collapses the continuum onto δ, answering the question of Carlson and Laver. Next we prove that if a proper forcing of the size at most continuum collapses ω 2 then it forces ◇ ω1 . ",

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More forcing notions imply diamond

Abstract

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