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 | English |
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Pages (from-to) | 373-384 |
Number of pages | 12 |
Journal | Archive for Mathematical Logic |
Volume | 55 |
Issue number | 3-4 |
DOIs | |
State | Published - 1 May 2016 |
Bibliographical note
Publisher Copyright:© 2015, Springer-Verlag Berlin Heidelberg.
Keywords
- Forcing
- Large cardinals
- Prikry type forcing