Switch to: References

Citations of:

Partitions and filters

Journal of Symbolic Logic 51 (1):12-21 (1986)

Add citations

You must login to add citations.
  1. Around splitting and reaping for partitions of ω.Hiroaki Minami - 2010 - Archive for Mathematical Logic 49 (4):501-518.
    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 (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Exactly two and exactly three near-coherence classes.Heike Mildenberger - 2023 - Journal of Mathematical Logic 24 (1).
    We prove that for [Formula: see text] and [Formula: see text] there is a forcing extension with exactly n near-coherence classes of non-principal ultrafilters. We introduce localized versions of Matet forcing and we develop Ramsey spaces of names. The evaluation of some of the new forcings is based on a relative of Hindman’s theorem due to Blass 1987.
    Download  
     
    Export citation  
     
    Bookmark  
  • Ramsey degrees of ultrafilters, pseudointersection numbers, and the tools of topological Ramsey spaces.Natasha Dobrinen & Sonia Navarro Flores - 2022 - Archive for Mathematical Logic 61 (7):1053-1090.
    This paper investigates properties of \(\sigma \) -closed forcings which generate ultrafilters satisfying weak partition relations. The Ramsey degree of an ultrafilter \({\mathcal {U}}\) for _n_-tuples, denoted \(t({\mathcal {U}},n)\), is the smallest number _t_ such that given any \(l\ge 2\) and coloring \(c:[\omega ]^n\rightarrow l\), there is a member \(X\in {\mathcal {U}}\) such that the restriction of _c_ to \([X]^n\) has no more than _t_ colors. Many well-known \(\sigma \) -closed forcings are known to generate ultrafilters with finite Ramsey degrees, (...)
    Download  
     
    Export citation  
     
    Bookmark  
  • Partition numbers.Otmar Spinas - 1997 - Annals of Pure and Applied Logic 90 (1-3):243-262.
    We continue [21] and study partition numbers of partial orderings which are related to /fin. In particular, we investigate Pf, be the suborder of /fin)ω containing only filtered elements, the Mathias partial order M, and , ω the lattice of partitions of ω, respectively. We show that Solomon's inequality holds for M and that it consistently fails for Pf. We show that the partition number of is C. We also show that consistently the distributivity number of ω is smaller than (...)
    Download  
     
    Export citation  
     
    Bookmark   9 citations  
  • On Shattering, Splitting and Reaping Partitions.Lorenz Halbeisen - 1998 - Mathematical Logic Quarterly 44 (1):123-134.
    Download  
     
    Export citation  
     
    Bookmark   4 citations  
  • Increasing the groupwise density number by c.c.c. forcing.Heike Mildenberger & Saharon Shelah - 2007 - Annals of Pure and Applied Logic 149 (1-3):7-13.
    Download  
     
    Export citation  
     
    Bookmark   1 citation  
  • Splittings.A. Kamburelis & B. W’Glorz - 1996 - Archive for Mathematical Logic 35 (4):263-277.
    We investigate some notions of splitting families and estimate sizes of the corresponding cardinal coefficients. In particular we solve a problem of P. Simon.
    Download  
     
    Export citation  
     
    Bookmark   14 citations  
  • A generalization of the Dual Ellentuck Theorem.Lorenz Halbeisen & Pierre Matet - 2003 - Archive for Mathematical Logic 42 (2):103-128.
    We prove versions of the Dual Ramsey Theorem and the Dual Ellentuck Theorem for families of partitions which are defined in terms of games.
    Download  
     
    Export citation  
     
    Bookmark