27 found
Order:
  1.  36
    Mad Families, Splitting Families and Large Continuum.Jörg Brendle & Vera Fischer - 2011 - Journal of Symbolic Logic 76 (1):198 - 208.
    Let κ < λ be regular uncountable cardinals. Using a finite support iteration (in fact a matrix iteration) of ccc posets we obtain the consistency of b = a = κ < s = λ. If μ is a measurable cardinal and μ < κ < λ, then using similar techniques we obtain the consistency of b = κ < a = s = λ.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   9 citations  
  2.  9
    Forcing Indestructibility of MAD Families.Jörg Brendle & Shunsuke Yatabe - 2005 - Annals of Pure and Applied Logic 132 (2):271-312.
    Let A[ω]ω be a maximal almost disjoint family and assume P is a forcing notion. Say A is P-indestructible if A is still maximal in any P-generic extension. We investigate P-indestructibility for several classical forcing notions P. In particular, we provide a combinatorial characterization of P-indestructibility and, assuming a fragment of MA, we construct maximal almost disjoint families which are P-indestructible yet Q-destructible for several pairs of forcing notions . We close with a detailed investigation of iterated Sacks indestructibility.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  3.  23
    Countable Fréchet Boolean Groups: An Independence Result.Jörg Brendle & Michael Hrušák - 2009 - Journal of Symbolic Logic 74 (3):1061-1068.
    It is relatively consistent with ZFC that every countable $FU_{fin} $ space of weight N₁ is metrizable. This provides a partial answer to a question of G. Gruenhage and P. Szeptycki [GS1].
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   7 citations  
  4.  43
    Solovay-Type Characterizations for Forcing-Algebras.Jörg Brendle & Benedikt Löwe - 1999 - Journal of Symbolic Logic 64 (3):1307-1323.
    We give characterizations for the sentences "Every $\Sigma^1_2$-set is measurable" and "Every $\Delta^1_2$-set is measurable" for various notions of measurability derived from well-known forcing partial orderings.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  5.  18
    Mob Families and Mad Families.Jörg Brendle - 1998 - Archive for Mathematical Logic 37 (3):183-197.
    We show the consistency of ${\frak o} <{\frak d}$ where ${\frak o}$ is the size of the smallest off-branch family, and ${\frak d}$ is as usual the dominating number. We also prove the consistency of ${\frak b} < {\frak a}$ with large continuum. Here, ${\frak b}$ is the unbounding number, and ${\frak a}$ is the almost disjointness number.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   12 citations  
  6.  20
    Bounding, Splitting, and Almost Disjointness.Jörg Brendle & Dilip Raghavan - 2014 - Annals of Pure and Applied Logic 165 (2):631-651.
    We investigate some aspects of bounding, splitting, and almost disjointness. In particular, we investigate the relationship between the bounding number, the closed almost disjointness number, the splitting number, and the existence of certain kinds of splitting families.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  7. The Cofinality of the Infinite Symmetric Group and Groupwise Density.Jörg Brendle & Maria Losada - 2003 - Journal of Symbolic Logic 68 (4):1354-1361.
    We show that g ≤ c(Sym(ω)) where g is the groupwise density number and c(Sym(ω)) is the cofinality of the infinite symmetric group. This solves (the second half of) a problem addressed by Thomas.
    Direct download (10 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  8. Amoeba-Absoluteness and Projective Measurability.Jörg Brendle - 1993 - Journal of Symbolic Logic 58 (4):1284-1290.
    We show that Σ1 4-Amoeba-absoluteness implies that $\forall a \in \mathbb{R}(\omega^{L\lbrack a \rbrack}_1 < \omega^V_1)$ and, hence, Σ1 3-measurability. This answers a question of Haim Judah (private communication).
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  9.  8
    Combinatorial Properties of Hechler Forcing.Jörg Brendle, Haim Judah & Saharon Shelah - 1992 - Annals of Pure and Applied Logic 58 (3):185-199.
    Brendle, J., H. Judah and S. Shelah, Combinatorial properties of Hechler forcing, Annals of Pure and Applied Logic 59 185–199. Using a notion of rank for Hechler forcing we show: assuming ωV1 = ωL1, there is no real in V[d] which is eventually different from the reals in L[ d], where d is Hechler over V; adding one Hechler real makes the invariants on the left-hand side of Cichoń's diagram equal ω1 and those on the right-hand side equal 2ω and (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   10 citations  
  10.  14
    Regularity Properties for Dominating Projective Sets.Jörg Brendle, Greg Hjorth & Otmar Spinas - 1995 - Annals of Pure and Applied Logic 72 (3):291-307.
    We show that every dominating analytic set in the Baire space has a dominating closed subset. This improves a theorem of Spinas [15] saying that every dominating analytic set contains the branches of a uniform tree, i.e. a superperfect tree with the property that for every splitnode all the successor splitnodes have the same length. In [15], a subset of the Baire space is called u-regular if either it is not dominating or it contains the branches of a uniform tree, (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   8 citations  
  11.  6
    Mad Families Constructed From Perfect Almost Disjoint Families.Jörg Brendle & Yurii Khomskii - 2013 - Journal of Symbolic Logic 78 (4):1164-1180.
  12.  11
    Van Douwen’s Diagram for Dense Sets of Rationals.Jörg Brendle - 2006 - Annals of Pure and Applied Logic 143 (1):54-69.
    We investigate cardinal invariants related to the structure of dense sets of rationals modulo the nowhere dense sets. We prove that , thus dualizing the already known [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the rationals, Fund. Math. 183 59–80, Theorem 3.6]. We also show the consistency of each of and . Our results answer four questions of Balcar, Hernández and Hrušák [B. Balcar, F. Hernández-Hernández, M. Hrušák, Combinatorics of dense subsets of the rationals, Fund. Math. (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  13.  17
    Cardinal Invariants of the Continuum and Combinatorics on Uncountable Cardinals.Jörg Brendle - 2006 - Annals of Pure and Applied Logic 144 (1):43-72.
    We explore the connection between combinatorial principles on uncountable cardinals, like stick and club, on the one hand, and the combinatorics of sets of reals and, in particular, cardinal invariants of the continuum, on the other hand. For example, we prove that additivity of measure implies that Martin’s axiom holds for any Cohen algebra. We construct a model in which club holds, yet the covering number of the null ideal is large. We show that for uncountable cardinals κ≤λ and , (...)
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  14.  9
    Construction with opposition: cardinal invariants and games.Jörg Brendle, Michael Hrušák & Víctor Torres-Pérez - 2019 - Archive for Mathematical Logic 58 (7):943-963.
    We consider several game versions of the cardinal invariants \, \ and \. We show that the standard proof that parametrized diamond principles prove that the cardinal invariants are small actually shows that their game counterparts are small. On the other hand we show that \ and \ are both relatively consistent with ZFC, where \ and \ are the principal game versions of \ and \, respectively. The corresponding question for \ remains open.
    No categories
    Direct download (2 more)  
    Translate
     
     
    Export citation  
     
    Bookmark  
  15.  11
    Combinatorial Properties of Classical Forcing Notions.Jörg Brendle - 1995 - Annals of Pure and Applied Logic 73 (2):143-170.
    We investigate the effect of adding a single real on cardinal invariants associated with the continuum. We show:1. adding an eventually different or a localization real adjoins a Luzin set of size continuum and a mad family of size ω1;2. Laver and Mathias forcing collapse the dominating number to ω1, and thus two Laver or Mathias reals added iteratively always force CH;3. Miller's rational perfect set forcing preserves the axiom MA.
    Direct download (6 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  16.  2
    Larger Cardinals in Cichon's Diagram.Jorg Brendle - 1991 - Journal of Symbolic Logic 56 (3):795.
    We prove that in many situations it is consistent with ZFC that part of the invariants involved in Cichon's diagram are equal to $\kappa$ while the others are equal to $\lambda$, where $\kappa < \lambda$ are both arbitrary regular uncountable cardinals. We extend some of these results to the case when $\lambda$ is singular. We also show that $\mathrm{cf}) < \kappa_A$ is consistent with ZFC.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  17.  22
    Martin's Axiom and the Dual Distributivity Number.Jörg Brendle - 2000 - Mathematical Logic Quarterly 46 (2):241-248.
    We show that it is consistent that Martin's axiom holds, the continuum is large, and yet the dual distributivity number ℌ is κ1. This answers a question of Halbeisen.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  18.  3
    Polarized Partitions on the Second Level of the Projective Hierarchy.Jörg Brendle & Yurii Khomskii - 2012 - Annals of Pure and Applied Logic 163 (9):1345-1357.
  19.  12
    Towers in Filters, Cardinal Invariants, and Luzin Type Families.Jörg Brendle, Barnabás Farkas & Jonathan Verner - 2018 - Journal of Symbolic Logic 83 (3):1013-1062.
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  20.  13
    Larger Cardinals in Cichoń's Diagram.Jörg Brendle - 1991 - Journal of Symbolic Logic 56 (3):795-810.
    We prove that in many situations it is consistent with ZFC that part of the invariants involved in Cichon's diagram are equal to κ while the others are equal to λ, where $\kappa < \lambda$ are both arbitrary regular uncountable cardinals. We extend some of these results to the case when λ is singular. We also show that $\mathrm{cf}(\kappa_U(\mathscr{L})) < \kappa_A(\mathscr{M})$ is consistent with ZFC.
    Direct download (7 more)  
     
    Export citation  
     
    Bookmark   3 citations  
  21.  16
    Converse Dual Cardinals.Jörg Brendle & Shuguo Zhang - 2006 - Journal of Symbolic Logic 71 (1):22 - 34.
    We investigate the set (ω) of partitions of the natural numbers ordered by ≤* where A ≤* B if by gluing finitely many blocks of A we can get a partition coarser than B. In particular, we determine the values of a number of cardinals which are naturally associated with the structure ((ω),≥*), in terms of classical cardinal invariants of the continuum.
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  22.  15
    Maximal Trees.Jörg Brendle - 2018 - Archive for Mathematical Logic 57 (3-4):421-428.
    We show that, consistently, there can be maximal subtrees of \\) and \ / {\mathrm {fin}}\) of arbitrary regular uncountable size below the size of the continuum \. We also show that there are no maximal subtrees of \ / {\mathrm {fin}}\) with countable levels. Our results answer several questions of Campero-Arena et al..
    No categories
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark  
  23.  28
    Evasion and Prediction.Jörg Brendle & Saharon Shelah - 2003 - Archive for Mathematical Logic 42 (4):349-360.
    . Say that a function π:n<ω→n k-constantly predicts a real xnω if for almost all intervals I of length k, there is iI such that x=π. We study the k-constant prediction number vnconst, that is, the size of the least family of predictors needed to k-constantly predict all reals, for different values of n and k, and investigate their relationship.
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  24.  21
    A Base-Matrix Lemma for Sets of Rationals Modulo Nowhere Dense Sets.Jörg Brendle & Diana Carolina Montoya - 2012 - Archive for Mathematical Logic 51 (3-4):305-317.
    We study some properties of the quotient forcing notions ${Q_{tr(I)} = \wp(2^{< \omega})/tr(I)}$ and P I = B(2 ω )/I in two special cases: when I is the σ-ideal of meager sets or the σ-ideal of null sets on 2 ω . We show that the remainder forcing R I = Q tr(I)/P I is σ-closed in these cases. We also study the cardinal invariant of the continuum ${\mathfrak{h}_{\mathbb{Q}}}$ , the distributivity number of the quotient ${Dense(\mathbb{Q})/nwd}$ , in order to (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  25.  6
    Cardinal Invariants of Infinite Groups.Jörg Brendle - 1990 - Archive for Mathematical Logic 30 (3):155-170.
    LetG be a group. CallG akC-group if every element ofG has less thank conjugates. Denote byP(G) the least cardinalk such that any subset ofG of sizek contains two elements which commute.It is shown that the existence of groupsG such thatP(G) is a singular cardinal is consistent withZFC. So is the existence of groupsG which are notkC but haveP(G) (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  26. Cardinal Invariants of Infinite Groups* Jorg Brendle Mathematisches Institut der Universitat Tubingen, Auf der Morgenstelle 10, W-7400 Tubingen, Federal Republic of Germany and Department of Mathematics and Computer Science, Bradley Hall, Dartmouth College, Hanover, NH 03755, USA. [REVIEW]Jorg Brendle - 1991 - Archive for Mathematical Logic 30:155-170.
    No categories
     
    Export citation  
     
    Bookmark  
  27. Proceedings of the 14th and 15th Asian Logic Conferences.Byunghan Kim, Jörg Brendle, Gyesik Lee, Fenrong Liu, R. Ramanujam, Shashi M. Srivastava, Akito Tsuboi & Liang Yu (eds.) - 2019
    No categories
     
    Export citation  
     
    Bookmark