Ultrafilters on -their ideals and their cardinal characteristics

Authors:
Saharon Shelah, Jörg Brendle and Saharon Shelah

Journal:
Trans. Amer. Math. Soc. **351** (1999), 2643-2674

MSC (1991):
Primary 03E05, 03E35

DOI:
https://doi.org/10.1090/S0002-9947-99-02257-6

Published electronically:
March 8, 1999

MathSciNet review:
1686797

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Abstract | References | Similar Articles | Additional Information

Abstract: For a free ultrafilter on we study several cardinal characteristics which describe part of the combinatorial structure of . We provide various consistency results; e.g. we show how to force simultaneously many characters and many -characters. We also investigate two ideals on the Baire space naturally related to and calculate cardinal coefficients of these ideals in terms of cardinal characteristics of the underlying ultrafilter.

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Additional Information

**Jörg Brendle**

Affiliation:
Department of Mathematics, Dartmouth College, Bradley Hall, Hanover, New Hampshire 03755

Address at time of publication:
Graduate School of Science and Technology, Kobe University, Rokko–dai, Nada, Kobe 657-8501, Japan

Email:
brendle@pascal.seq.kobe-u.ac.jp

**Saharon Shelah**

Affiliation:
Institute of Mathematics, The Hebrew University, Jerusalem 91904, Israel;
Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903

DOI:
https://doi.org/10.1090/S0002-9947-99-02257-6

Keywords:
Ultrafilter,
$P$--point,
Ramsey ultrafilter,
character,
$\pi $--character,
ideal,
Ramsey null sets (nowhere Ramsey sets),
cardinal coefficient,
Mathias forcing,
Laver forcing,
Easton forcing

Received by editor(s):
March 10, 1997

Received by editor(s) in revised form:
November 4, 1997

Published electronically:
March 8, 1999

Additional Notes:
The research of the first author was partially supported by DFG–grant Nr. Br 1420/1–1.

The research of the second author was supported by the German–Israeli Foundation for Scientific Research & Development Grant No. G-294.081.06/93. Publication 642 on the second author’s list of publications.

Article copyright:
© Copyright 1999
American Mathematical Society