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- Publisher
- Springer Journals
- Copyright
- Copyright © 2010 by Springer-Verlag
- Subject
- Mathematics; Algebra; Mathematics, general; Mathematical Logic and Foundations
- ISSN
- 0933-5846
- eISSN
- 1432-0665
- DOI
- 10.1007/s00153-010-0184-9
- Publisher site
- See Article on Publisher Site
Abstract
We investigate splitting number and reaping number for the structure (ω) ω of infinite partitions of ω. We prove that $${\mathfrak{r}_{d}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N}),\mathfrak{d}}$$ and $${\mathfrak{s}_{d}\geq\mathfrak{b}}$$ . We also show the consistency results $${\mathfrak{r}_{d} > \mathfrak{b}, \mathfrak{s}_{d} < \mathfrak{d}, \mathfrak{s}_{d} < \mathfrak{r}, \mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}$$ and $${\mathfrak{s}_{d} > \mathsf{cof}(\mathcal{M})}$$ . To prove the consistency $${\mathfrak{r}_{d} < \mathsf{add}(\mathcal{M})}$$ and $${\mathfrak{s}_{d} < \mathsf{cof}(\mathcal{M})}$$ we introduce new cardinal invariants $${\mathfrak{r}_{pair}}$$ and $${\mathfrak{s}_{pair}}$$ . We also study the relation between $${\mathfrak{r}_{pair}, \mathfrak{s}_{pair}}$$ and other cardinal invariants. We show that $${\mathsf{cov}(\mathcal{M}),\mathsf{cov}(\mathcal{N})\leq\mathfrak{r}_{pair}\leq\mathfrak{s}_{d},\mathfrak{r}}$$ and $${\mathfrak{s}\leq\mathfrak{s}_{pair}\leq\mathsf{non}(\mathcal{M}),\mathsf{non}(\mathcal{N})}$$ .
Journal
Archive for Mathematical Logic – Springer Journals
Published: Mar 27, 2010