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On some new ideals on the Cantor and Baire spaces

Author(s): Jacek Cichon; Jan Kraszewski
Journal: Proc. Amer. Math. Soc. 126 (1998), 1549-1555.
MSC (1991): Primary 04A20, 28A05
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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.

References:

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 $\operatorname{in}$ 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 Wrocl{}aw, pl. Grunwaldzki~2/4, 50-156 Wrocl{}aw, Poland
Email: cichon@math.uni.wroc.pl

Jan Kraszewski
Affiliation: Department of Mathematics, University of Wrocl{}aw, pl. Grunwaldzki~2/4, 50-156 Wrocl{}aw, Poland
Email: kraszew@math.uni.wroc.pl

DOI: 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 Wrocl{}aw.
Communicated by: Andreas R. Blass
Copyright of article: Copyright 1998, American Mathematical Society


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