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Combinatorial aspects of F$_\sigma $ filters
with an application to $\mathcal {N}$-sets


Author: Claude Laflamme
Journal: Proc. Amer. Math. Soc. 125 (1997), 3019-3025
MSC (1991): Primary 04A20; Secondary 03E05, 03E15, 03E35
DOI: https://doi.org/10.1090/S0002-9939-97-03926-9
MathSciNet review: 1401747
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Abstract: We discuss F$_\sigma $ filters and show that the minimum size of a filter base generating an undiagonalizable filter included in some F$_\sigma $ filter is the better known bounded evasion number ${\frak e}_{ubd}$. An application to $\mathcal {N}$-sets from trigonometric series is given by showing that if $A$ is an $\mathcal {N}$-set and $B$ has size less than ${\frak e}_{ubd}$, then $A \cup B$ is again an ${\cal N}$-set.


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Additional Information

Claude Laflamme
Affiliation: Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada T2N 1N4
Email: laflamme@acs.ucalgary.ca

DOI: https://doi.org/10.1090/S0002-9939-97-03926-9
Received by editor(s): September 18, 1995
Received by editor(s) in revised form: May 1, 1996
Additional Notes: This research was partially supported by NSERC of Canada.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 1997 American Mathematical Society

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