A version of κ -Miller forcing

Heike Mildenberger; Saharon Shelah

doi:10.1007/s00153-020-00721-y

A version of κ -Miller forcing

Heike Mildenberger^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

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

1 Scopus citations

Abstract

We consider a version of κ-Miller forcing on an uncountable cardinal κ. We show that under 2 ^<^κ= κ this forcing collapses 2 ^κ to ω and adds a κ-Cohen real. The same holds under the weaker assumptions that cf(κ)>ω, 22<κ=2κ, and forcing with ([κ] ^κ, ⊆) collapses 2 ^κ to ω.

Original language	English
Pages (from-to)	879-892
Number of pages	14
Journal	Archive for Mathematical Logic
Volume	59
Issue number	7-8
DOIs	https://doi.org/10.1007/s00153-020-00721-y
State	Published - 1 Nov 2020

Bibliographical note

Publisher Copyright:
© 2020, The Author(s).

Keywords

Forcing with higher perfect trees

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10.1007/s00153-020-00721-y

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AB - We consider a version of κ-Miller forcing on an uncountable cardinal κ. We show that under 2 <κ= κ this forcing collapses 2 κ to ω and adds a κ-Cohen real. The same holds under the weaker assumptions that cf(κ)>ω, 22<κ=2κ, and forcing with ([κ] κ, ⊆) collapses 2 κ to ω.

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A version of κ -Miller forcing

Abstract

Bibliographical note

Keywords

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