Ultrafilters on the natural numbers

Journal of Symbolic Logic 68 (3):764-784 (2003)
  Copy   BIBTEX


We study the problem of existence and generic existence of ultrafilters on ω. We prove a conjecture of $J\ddot{o}rg$ Brendle's showing that there is an ultrafilter that is countably closed but is not an ordinal ultrafilter under CH. We also show that Canjar's previous partial characterization of the generic existence of Q-points is the best that can be done. More simply put, there is no normal cardinal invariant equality that fully characterizes the generic existence of Q-points. We then sharpen results on generic existence with the introduction of $\sigma-compact$ ultrafilters. We show that the generic existence of said ultrafilters is equivalent to $\delta = c$ . This result taken along with our result that there exists a $K_{\sigma}$ non-countably closed ultrafilter under CH, expands the size of the class of ultrafilters that were known to fit this description before. From the core of the proof, we get a new result on the cardinal invariants of the continuum, i.e., the cofinality of the sets with $\sigma-compact$ closure is δ



    Upload a copy of this work     Papers currently archived: 89,378

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Forcing and stable ordered–union ultrafilters.Todd Eisworth - 2002 - Journal of Symbolic Logic 67 (1):449-464.
Ultrafilters which extend measures.Michael Benedikt - 1998 - Journal of Symbolic Logic 63 (2):638-662.
Saturating ultrafilters on N.D. H. Fremlin & P. J. Nyikos - 1989 - Journal of Symbolic Logic 54 (3):708-718.
On Milliken-Taylor Ultrafilters.Heike Mildenberger - 2011 - Notre Dame Journal of Formal Logic 52 (4):381-394.
On the cofinality of ultrapowers.Andreas Blass & Heike Mildenberger - 1999 - Journal of Symbolic Logic 64 (2):727-736.
A few special ordinal ultrafilters.Claude Laflamme - 1996 - Journal of Symbolic Logic 61 (3):920-927.
Ultrafilters on ω.James E. Baumgartner - 1995 - Journal of Symbolic Logic 60 (2):624-639.


Added to PP

48 (#288,462)

6 months
4 (#306,312)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

Cascades, order, and ultrafilters.Andrzej Starosolski - 2014 - Annals of Pure and Applied Logic 165 (10):1626-1638.

Add more citations

References found in this work

Set Theory.Thomas Jech - 1999 - Studia Logica 63 (2):300-300.

Add more references