5 found
Order:
  1.  42
    Mathias–Prikry and Laver–Prikry Type Forcing.Michael Hrušák & Hiroaki Minami - 2014 - Annals of Pure and Applied Logic 165 (3):880-894.
    We study the Mathias–Prikry and Laver–Prikry forcings associated with filters on ω. We give a combinatorial characterization of Martinʼs number for these forcing notions and present a general scheme for analyzing preservation properties for them. In particular, we give a combinatorial characterization of those filters for which the Mathias–Prikry forcing does not add a dominating real.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   5 citations  
  2.  86
    Pair-Splitting, Pair-Reaping and Cardinal Invariants of F Σ -Ideals.Michael Hrušák, David Meza-Alcántara & Hiroaki Minami - 2010 - Journal of Symbolic Logic 75 (2):661-677.
    We investigate the pair-splitting number $\germ{s}_{pair}$ which is a variation of splitting number, pair-reaping number $\germ{r}_{pair}$ which is a variation of reaping number and cardinal invariants of ideals on ω. We also study cardinal invariants of F σ ideals and their upper bounds and lower bounds. As an application, we answer a question of S. Solecki by showing that the ideal of finitely chromatic graphs is not locally Katětov-minimal among ideals not satisfying Fatou's lemma.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   6 citations  
  3.  62
    Diamond Principles in Cichoń’s Diagram.Hiroaki Minami - 2004 - Archive for Mathematical Logic 44 (4):513-526.
    We present several models which satisfy CH and some ♦-like principles while others fail, answering a question of Moore, Hrušák and Džamonja.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  4.  52
    Suslin Forcing and Parametrized ♢ Principles.Hiroaki Minami - 2008 - Journal of Symbolic Logic 73 (3):752-764.
    By using finite support iteration Suslin c.c.c forcing notions we construct several models which satisfy some ♢-like principles while other cardinal invariants are larger than ω1.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark  
  5.  55
    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 (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark