Rendiconti del Circolo Matematico di Palermo

, Volume 60, Issue 3, pp 445–454 | Cite as

Adding ultrafilters by definable quotients

Article

Abstract

Forcing notions of the type \(\mathcal{P}(\omega)/\mathcal{I}\) which do not add reals naturally add ultrafilters on ω. We investigate what classes of ultrafilters can be added in this way when \(\mathcal{I}\) is a definable ideal. In particular, we show that if \(\mathcal{I}\) is an Fσ P-ideal the generic ultrafilter will be a P-point without rapid RK-predecessors which is not a strong P-point. This provides an answer to long standing open questions of Canjar and Laflamme.

Keywords

Ultrafilter P-point Q-point Selective ultrafilter Rapid ultrafilter Fσ-ideal 

Mathematics Subject Classification (2000)

O3E05 03E17 03E35 

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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Instituto de MatemáticasUNAMMoreliaMéxico
  2. 2.KTIMLCharles UniversityPraha 1Czech Republic

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