12 found
Order:
  1.  5
    Creature Forcing and Five Cardinal Characteristics in Cichoń’s Diagram.Arthur Fischer, Martin Goldstern, Jakob Kellner & Saharon Shelah - 2017 - Archive for Mathematical Logic 56 (7-8):1045-1103.
    We use a creature construction to show that consistently $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$The same method shows the consistency of $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.
    No categories
    Direct download (5 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  2.  20
    Continuous Ramsey Theory on Polish Spaces and Covering the Plane by Functions.Stefan Geschke, Martin Goldstern & Menachem Kojman - 2004 - Journal of Mathematical Logic 4 (2):109-145.
  3.  19
    The Bounded Proper Forcing Axiom.Martin Goldstern & Saharon Shelah - 1995 - Journal of Symbolic Logic 60 (1):58-73.
    The bounded proper forcing axiom BPFA is the statement that for any family of ℵ 1 many maximal antichains of a proper forcing notion, each of size ℵ 1 , there is a directed set meeting all these antichains. A regular cardinal κ is called Σ 1 -reflecting, if for any regular cardinal χ, for all formulas $\varphi, "H(\chi) \models`\varphi'"$ implies " $\exists\delta . We investigate several algebraic consequences of BPFA, and we show that the consistency strength of the bounded (...)
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   16 citations  
  4.  13
    Mikhail G. Peretyat'Kin. Konechno Aksiomatiziruemye Teorii. Russian Original of the Preceding. Sibirskaya Shkola Algebry I Logiki. Nauchnaya Kniga, Novosibirsk1997, 322 + Xiv Pp. - F. R. Drake and D. Singh. Intermediate Set Theory. John Wiley & Sons, Chichester, New York, Etc., 1996, X + 234 Pp. - Winfried Just and Martin Weese. Discovering Modern Set Theory. II. Set-Theoretic Tools for Every Mathematician. Graduate Studies in Mathematics, Vol. 18. American Mathematical Society, Providence1997, Xiii + 224 Pp. [REVIEW]Martin Goldstern - 1999 - Journal of Symbolic Logic 64 (4):1830-1832.
  5.  7
    Set Theory, Annual Boise Extravaganza in Set Theory Conference, March 13–15, 1992, April 10–11, 1993, March 25–27,1994, Boise State University, Boise, Idaho, Edited by Tomek Bartoszyński and Marion Scheepers, Contemporary Mathematics, Vol. 192, American Mathematical Society, Providence1996, Xii + 184 Pp. [REVIEW]Martin Goldstern - 1997 - Journal of Symbolic Logic 62 (2):680-683.
  6.  3
    New Reals: Can Live with Them, Can Live Without Them.Martin Goldstern & Jakob Kellner - 2006 - Mathematical Logic Quarterly 52 (2):115-124.
    We give a self-contained proof of the preservation theorem for proper countable support iterations known as “tools-preservation”, “Case A” or “first preservation theorem” in the literature. We do not assume that the forcings add reals.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   4 citations  
  7.  23
    Many Simple Cardinal Invariants.Martin Goldstern & Saharon Shelah - 1993 - Archive for Mathematical Logic 32 (3):203-221.
  8.  45
    Strong Measure Zero Sets Without Cohen Reals.Martin Goldstern, Haim Judah & Saharon Shelah - 1993 - Journal of Symbolic Logic 58 (4):1323-1341.
    If ZFC is consistent, then each of the following is consistent with ZFC + 2ℵ0 = ℵ2: (1) $X \subseteq \mathbb{R}$ is of strong measure zero iff |X| ≤ ℵ1 + there is a generalized Sierpinski set. (2) The union of ℵ1 many strong measure zero sets is a strong measure zero set + there is a strong measure zero set of size ℵ2 + there is no Cohen real over L.
    Direct download (9 more)  
     
    Export citation  
     
    Bookmark   2 citations  
  9.  17
    Strongly Amorphous Sets and Dual Dedekind Infinity.Martin Goldstern - 1997 - Mathematical Logic Quarterly 43 (1):39-44.
    1. If A is strongly amorphous , then its power set P is dually Dedekind infinite, i. e., every function from P onto P is injective. 2. The class of “inexhaustible” sets is not closed under supersets unless AC holds.
    Direct download (4 more)  
     
    Export citation  
     
    Bookmark   1 citation  
  10.  6
    [Omnibus Review].Martin Goldstern - 1997 - Journal of Symbolic Logic 62 (2):680-683.
    Reviewed Works:Tomek Bartoszynski, Marion Scheepers, Set Theory, Annual Boise Extravaganza in Set Theory Conference, March 13-15, 1992, April 10-11, 1993, March 25-27, 1994, Boise State University, Boise, Idaho.R. Aharoni, A. Hajnal, E. C. Milner, Interval Covers of a Linearly Ordered Set.Eyal Amir, Haim Judah, Souslin Absoluteness, Uniformization and Regularity Properties of Projective Sets.Tomek Bartoszynski, Ireneusz Reclaw, Not Every $\gamma$-Set is Strongly Meager.Andreas Blass, Reductions Between Cardinal Characteristics of the Continuum.Claude Laflamme, Filter Games and Combinatorial Properties of Strategies.R. Daniel Mauldin, Analytic (...)
    Direct download (3 more)  
     
    Export citation  
     
    Bookmark  
  11.  6
    Review: Mikhail G. Peretyat'kin, Konechno Aksiomatiziruemye Teorii; F. R. Drake, D. Singh, Intermediate Set Theory; Winfried Just, Martin Weese, Discovering Modern Set Theory. II. Set-Theoretic Tools for Every Mathematician. [REVIEW]Martin Goldstern - 1999 - Journal of Symbolic Logic 64 (4):1830-1832.
  12.  2
    Nijmegen, The Netherlands July 27–August 2, 2006.Rodney Downey, Ieke Moerdijk, Boban Velickovic, Samson Abramsky, Marat Arslanov, Harvey Friedman, Martin Goldstern, Ehud Hrushovski, Jochen Koenigsmann & Andy Lewis - 2007 - Bulletin of Symbolic Logic 13 (2).
    Direct download (2 more)  
     
    Export citation  
     
    Bookmark