Restrictions on forcings that change cofinalities

Yair Hayut; Asaf Karagila

doi:10.1007/s00153-015-0454-7

Restrictions on forcings that change cofinalities

Yair Hayut, Asaf Karagila^*

^*Corresponding author for this work

Einstein Institute of Mathematics

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

4 Scopus citations

Abstract

In this paper we investigate some properties of forcing which can be considered “nice” in the context of singularizing regular cardinals to have an uncountable cofinality. We show that such forcing which changes cofinality of a regular cardinal, cannot be too nice and must cause some “damage” to the structure of cardinals and stationary sets. As a consequence there is no analogue to the Prikry forcing, in terms of “nice” properties, when changing cofinalities to be uncountable.

Original language	American English
Pages (from-to)	373-384
Number of pages	12
Journal	Archive for Mathematical Logic
Volume	55
Issue number	3-4
DOIs	https://doi.org/10.1007/s00153-015-0454-7
State	Published - 1 May 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.

Keywords

Forcing
Large cardinals
Prikry type forcing

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10.1007/s00153-015-0454-7

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abstract = "In this paper we investigate some properties of forcing which can be considered “nice” in the context of singularizing regular cardinals to have an uncountable cofinality. We show that such forcing which changes cofinality of a regular cardinal, cannot be too nice and must cause some “damage” to the structure of cardinals and stationary sets. As a consequence there is no analogue to the Prikry forcing, in terms of “nice” properties, when changing cofinalities to be uncountable.",

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KW - Prikry type forcing

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Restrictions on forcings that change cofinalities

Abstract

Bibliographical note

Keywords

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