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On shattering, splitting and reaping partitions
[article]
2001
arXiv
pre-print
In this article we investigate the dual-shattering cardinal H, the dual-splitting cardinal S and the dual-reaping cardinal R, which are dualizations of the well-known cardinals h (the shattering cardinal, also known as the distributivity number of P(omega) modulo finite, s (the splitting number) and r (the reaping number). Using some properties of the ideal J of nowhere dual-Ramsey sets, which is an ideal over the set of partitions of omega, we show that add(J)=cov(J)=H. With this result we can
arXiv:math/0109099v1
fatcat:ekkttasrujcjhe4a5pnogybhay