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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Hayut, Y., Karagila, A. Restrictions on forcings that change cofinalities. Arch. Math. Logic 55, 373–384 (2016). https://doi.org/10.1007/s00153-015-0454-7
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DOI: https://doi.org/10.1007/s00153-015-0454-7