On two problems of Erdos and Hechler: New methods in singular madness
Authors:
Menachem Kojman, Wieslaw Kubis and Saharon Shelah
Journal:
Proc. Amer. Math. Soc. 132 (2004), 3357-3365
MSC (2000):
Primary 03E10, 03E04, 03E17, 03E35; Secondary 03E55, 03E50
DOI:
https://doi.org/10.1090/S0002-9939-04-07580-X
Published electronically:
June 21, 2004
MathSciNet review:
2073313
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Abstract | References | Similar Articles | Additional Information
Abstract: For an infinite cardinal ,
denotes the set of all cardinalities of nontrivial maximal almost disjoint families over
.
Erdos and Hechler proved in 1973 the consistency of for a singular cardinal
and asked if it was ever possible for a singular
that
, and also whether
for every singular cardinal
.
We introduce a new method for controlling for a singular
and, among other new results about the structure of
for singular
, settle both problems affirmatively.
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Additional Information
Menachem Kojman
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel
Email:
kojman@math.bgu.ac.il
Wieslaw Kubis
Affiliation:
Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva, Israel – and – Institute of Mathematics, University of Silesia, Katowice, Poland
Email:
kubis@math.bgu.ac.il
Saharon Shelah
Affiliation:
Institute of Mathematics, Hebrew University of Jerusalem, Israel – and – Department of Mathematics, Rutgers University, New Brunswick, New Jersey
Email:
shelah@math.huji.ac.il
DOI:
https://doi.org/10.1090/S0002-9939-04-07580-X
Keywords:
Almost disjoint family,
singular cardinal,
bounding number,
smooth pcf scales
Received by editor(s):
June 10, 2002
Received by editor(s) in revised form:
September 10, 2002
Published electronically:
June 21, 2004
Additional Notes:
The first author’s research partially supported by an Israeli Science Foundation grant no. 177/01
The third author’s research was supported by The Israel Science Foundation, Publication 793.
Communicated by:
Carl G. Jockusch, Jr.
Article copyright:
© Copyright 2004
American Mathematical Society