14 found
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  1.  13
    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 $$\begin{aligned} \mathfrak d=\aleph _1= {{\mathrm{cov}}}< {{\mathrm{non}}}< {{\mathrm{non}}}< {{\mathrm{cof}}} < 2^{\aleph _0}. \end{aligned}$$.
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  2.  59
    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 (...)
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  3.  26
    Many Simple Cardinal Invariants.Martin Goldstern & Saharon Shelah - 1993 - Archive for Mathematical Logic 32 (3):203-221.
  4.  35
    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.
    We investigate the Ramsey theory of continuous graph-structures on complete, separable metric spaces and apply the results to the problem of covering a plane by functions. Let the homogeneity number[Formula: see text] of a pair-coloring c:[X]2→2 be the number of c-homogeneous subsets of X needed to cover X. We isolate two continuous pair-colorings on the Cantor space 2ω, c min and c max, which satisfy [Formula: see text] and prove: Theorem. For every Polish space X and every continuous pair-coloringc:[X]2→2with[Formula: see (...)
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  5.  6
    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.
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  6.  48
    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.
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  7.  20
    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.
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  8.  4
    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).
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  9.  3
    Controlling Cardinal Characteristics Without Adding Reals.Martin Goldstern, Jakob Kellner, Diego A. Mejía & Saharon Shelah - forthcoming - Journal of Mathematical Logic:2150018.
    We investigate the behavior of cardinal characteristics of the reals under extensions that do not add new [Formula: see text]-sequences. As an application, we show that consistently the following cardinal characteristics can be different: The characteristics in Cichoń’s diagram, plus [Formula: see text].. We also give constructions to alternatively separate other MA-numbers, namely: MA for [Formula: see text]-Knaster from MA for [Formula: see text]-Knaster; and MA for the union of all [Formula: see text]-Knaster forcings from MA for precaliber.
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  10.  4
    Cichoń’s diagram and localisation cardinals.Martin Goldstern & Lukas Daniel Klausner - forthcoming - Archive for Mathematical Logic:1-69.
    We reimplement the creature forcing construction used by Fischer et al. :1045–1103, 2017. https://doi.org/10.1007/S00153-017-0553-8. arXiv:1402.0367 [math.LO]) to separate Cichoń’s diagram into five cardinals as a countable support product. Using the fact that it is of countable support, we augment our construction by adding uncountably many additional cardinal characteristics, sometimes referred to as localisation cardinals.
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  11.  23
    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.
  12.  8
    [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 (...)
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  13.  11
    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.
  14.  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.