Around splitting and reaping for partitions of omega

作者：Minami Hiroaki^*

来源：Archive for Mathematical Logic, 2010, 49(4): 501-518.

DOI：10.1007/s00153-010-0184-9

• Partitions of omega
• Cardinal invariants of continuum
• Dual-splitting number
• Dual-reaping number
• Pair-splitting number
• Pair-reaping number

We investigate splitting number and reaping number for the structure (omega)(omega) of infinite partitions of omega. We prove that r(d) <= non( M), non(N), d and s(d) >= b. We also show the consistency results r(d) > b, s(d) < d, s(d) < r, r(d) < add( M) and s(d) > cof( M). To prove the consistency r(d) < add(M) and s(d) < cof(M) we introduce new cardinal invariants r(pair) and s(pair). We also study the relation between r(pair), s(pair) and other cardinal invariants. We show that cov(M), cov(N) <= r(pair) <= s(d), r and s <= s(pair) <= non(M), non(N).

• 出版日期2010-5