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On some new ideals
on the Cantor and Baire spaces
Authors:
Jacek Cichon and Jan Kraszewski
Journal:
Proc. Amer. Math. Soc. 126 (1998), 1549-1555
MSC (1991):
Primary 04A20, \, 28A05
MathSciNet review:
1452798
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Abstract: We define and investigate some new ideals of subsets of the Cantor space and the Baire space. We show that combinatorial properties of these ideals can be described by the splitting and reaping cardinal numbers. We show that there exist perfect Luzin sets for these ideals on the Baire space.
- 1.
Jacek
Cichoń, On two-cardinal properties of
ideals, Trans. Amer. Math. Soc.
314 (1989), no. 2,
693–708. MR 1005527
(91a:04001), http://dx.doi.org/10.1090/S0002-9947-1989-1005527-X
- 2.
Cicho\'{n} J., Kharazishvili A.B., On ideals with projective bases, 1995 (to appear).
- 3.
Eric
K. van Douwen, The integers and topology, Handbook of
set-theoretic topology, North-Holland, Amsterdam, 1984,
pp. 111–167. MR 776622
(87f:54008)
- 1.
- Cicho\'{n} J., On two-cardinal properties of ideals, Trans. Amer. Math. Soc. 314 (1989), 693-708. MR 91a:04001
- 2.
- Cicho\'{n} J., Kharazishvili A.B., On ideals with projective bases, 1995 (to appear).
- 3.
- van Douwen E.K., The integers and topology
 Handbook of Set Theoretical Topology, K. Kunen and J. Vaughan, eds., North-Holland, Amsterdam (1984), 111-167. MR 87f:54008
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Additional Information
Jacek Cichon
Affiliation:
Department of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-156 Wrocław, Poland
Email:
cichon@math.uni.wroc.pl
Jan Kraszewski
Affiliation:
Department of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-156 Wrocław, Poland
Email:
kraszew@math.uni.wroc.pl
DOI:
http://dx.doi.org/10.1090/S0002-9939-98-04378-0
PII:
S 0002-9939(98)04378-0
Keywords:
Set theory,
ideals,
Borel sets,
Cantor space,
Baire space,
cardinal functions
Received by editor(s):
December 18, 1995
Received by editor(s) in revised form:
October 16, 1996
Additional Notes:
Research of the second author supported by a grant 2149/W/IM/96 from the University of Wrocław.
Communicated by:
Andreas R. Blass
Article copyright:
© Copyright 1998 American Mathematical Society
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