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Thin stationary sets and disjoint club sequences
Author(s):
Sy-David
Friedman;
John
Krueger
Journal:
Trans. Amer. Math. Soc.
359
(2007),
2407-2420.
MSC (2000):
Primary 03E35, 03E40
Posted:
December 5, 2006
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Abstract:
We describe two opposing combinatorial properties
related
to adding clubs to :
the existence of a thin stationary subset of
and the existence
of a
disjoint club sequence on .
A special Aronszajn tree on
implies there exists a thin stationary set.
If there exists a disjoint club sequence, then
there is no
thin stationary set, and moreover there is a fat
stationary subset
of which cannot acquire a
club subset
by any forcing poset which preserves and .
We prove that the existence of a disjoint club
sequence follows
from Martin's Maximum and is equiconsistent with
a Mahlo cardinal.
References:
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Additional Information:
Sy-David
Friedman
Affiliation:
Kurt Gödel Research Center for Mathematical Logic, University of Vienna, Waehringer Strasse 25, A-1090 Wien, Austria
Email:
sdf@logic.univie.ac.at
John
Krueger
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Email:
jkrueger@math.berkeley.edu
DOI:
10.1090/S0002-9947-06-04163-8
PII:
S 0002-9947(06)04163-8
Received by editor(s):
June 28, 2005
Posted:
December 5, 2006
Additional Notes:
The authors were supported by FWF project number P16790-N04.
Copyright of article:
Copyright
2006,
American Mathematical Society
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