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Archive for Mathematical Logic

, Volume 55, Issue 3–4, pp 373–384 | Cite as

Restrictions on forcings that change cofinalities

  • Yair Hayut
  • Asaf Karagila
Article

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.

Keywords

Large cardinals Forcing Prikry type forcing 

Mathematics Subject Classification

Primary 03E35 Secondary 03E55 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Einstein Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

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