28 found
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  1.  3
    Hypergraphs and Proper Forcing.Jindřich Zapletal - forthcoming - Journal of Mathematical Logic.
    Given a Polish space X and a countable collection of analytic hypergraphs on X, I consider the σ-ideal generated by Borel anticliques for the hypergraphs in the family. It turns out that many of th...
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  2.  39
    Forcing with Quotients.Michael Hrušák & Jindřich Zapletal - 2008 - Archive for Mathematical Logic 47 (7-8):719-739.
    We study an extensive connection between quotient forcings of Borel subsets of Polish spaces modulo a σ-ideal and quotient forcings of subsets of countable sets modulo an ideal.
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  3.  33
    Isolating Cardinal Invariants.Jindřich Zapletal - 2003 - Journal of Mathematical Logic 3 (1):143-162.
    There is an optimal way of increasing certain cardinal invariants of the continuum.
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  4.  6
    Analytic Equivalence Relations and the Forcing Method.Jindřich Zapletal - 2013 - Bulletin of Symbolic Logic 19 (4):473-490.
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  5. Splitting Number at Uncountable Cardinals.Jindřich Zapletal - 1997 - Journal of Symbolic Logic 62 (1):35-42.
    We study a generalization of the splitting number s to uncountable cardinals. We prove that $\mathfrak{s}(\kappa) > \kappa^+$ for a regular uncountable cardinal κ implies the existence of inner models with measurables of high Mitchell order. We prove that the assumption $\mathfrak{s}(\aleph_\omega) > \aleph_{\omega + 1}$ has a considerable large cardinal strength as well.
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  6.  5
    More on the Cut and Choose Game.Jindřich Zapletal - 1995 - Annals of Pure and Applied Logic 76 (3):291-301.
    The cut and choose game is one of the infinitary games on a complete Boolean algebra B introduced by Jech. We prove that existence of a winning strategy for II in implies semiproperness of B. If the existence of a supercompact cardinal is consistent then so is “for every 1-distributive algebra B II has a winning strategy in ”.
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  7.  5
    Cofinalities of Borel Ideals.Michael Hrušák, Diego Rojas-Rebolledo & Jindřich Zapletal - 2014 - Mathematical Logic Quarterly 60 (1-2):31-39.
  8.  9
    Analytic Equivalence Relations and the Forcing Method.Jindřich Zapletal - 2013 - Bulletin of Symbolic Logic 19 (4):473-490.
    I describe several ways in which forcing arguments can be used to yield clean and conceptual proofs of nonreducibility, ergodicity and other results in the theory of analytic equivalence relations. In particular, I present simple Borel equivalence relations $E, F$ such that a natural proof of nonreducibility of $E$ to $F$ uses the independence of the Singular Cardinal Hypothesis at $\aleph_\omega$.
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  9.  12
    Proper Forcing and L(ℝ).Itay Neeman & Jindřich Zapletal - 2001 - Journal of Symbolic Logic 66 (2):801-810.
    We present two ways in which the model L(R) is canonical assuming the existence of large cardinals. We show that the theory of this model, with ordinal parameters, cannot be changed by small forcing; we show further that a set of ordinals in V cannot be added to L(R) by small forcing. The large cardinal needed corresponds to the consistency strength of AD L (R); roughly ω Woodin cardinals.
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  10.  3
    Four and More.Ilijas Farah & Jindřich Zapletal - 2006 - Annals of Pure and Applied Logic 140 (1):3-39.
    We isolate several large classes of definable proper forcings and show how they include many partial orderings used in practice.
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  11.  10
    Forcing Properties of Ideals of Closed Sets.Marcin Sabok & Jindřich Zapletal - 2011 - Journal of Symbolic Logic 76 (3):1075 - 1095.
    With every σ-ideal I on a Polish space we associate the σ-ideal I* generated by the closed sets in I. We study the forcing notions of Borel sets modulo the respective σ-ideals I and I* and find connections between their forcing properties. To this end, we associate to a σ-ideal on a Polish space an ideal on a countable set and show how forcing properties of the forcing depend on combinatorial properties of the ideal. We also study the 1—1 or (...)
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  12. Small Forcings and Cohen Reals.Jindřich Zapletal - 1997 - Journal of Symbolic Logic 62 (1):280-284.
    We show that all posets of uniform density ℵ 1 may have to add a Cohen real and develop some forcing machinery for obtaining this sort of result.
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  13.  2
    Increasing Δ 1 2 and Namba-Style Forcing.Richard Ketchersid, Paul Larson & Jindřich Zapletal - 2007 - Journal of Symbolic Logic 72 (4):1372-1378.
    We isolate a forcing which increases the value of δ12 while preserving ω₁ under the assumption that there is a precipitous ideal on ω₁ and a measurable cardinal.
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  14.  10
    Semi-Cohen Boolean Algebras.Bohuslav Balcar, Thomas Jech & Jindřich Zapletal - 1997 - Annals of Pure and Applied Logic 87 (3):187-208.
    We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semi-Cohen algebras, pseudo-Cohen algebras and potentially Cohen algebras. These classes of Boolean algebras are closed under completion.
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  15.  4
    Bounded Namba Forcing Axiom May Fail.Jindrich Zapletal - 2018 - Mathematical Logic Quarterly 64 (3):170-172.
    No categories
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  16.  16
    Proper Forcings and Absoluteness in LProper Forcing and L.Paul B. Larson, Itay Neeman & Jindrich Zapletal - 2002 - Bulletin of Symbolic Logic 8 (4):548.
  17.  19
    Preserving Σ-Ideals.Jindřich Zapletal - 1998 - Journal of Symbolic Logic 63 (4):1437-1441.
    It is proved consistent that there be a proper σ-ideal ℑ on ω 1 and an ℵ 1 -preserving poset P such that $\mathbb{P} \Vdash$ the σ-ideal generated by ℑ̌ is not proper.
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  18.  4
    Canonical Models for Fragments of the Axiom of Choice.Paul Larson & Jindřich Zapletal - 2017 - Journal of Symbolic Logic 82 (2):489-509.
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  19.  9
    Killing Ideals and Adding Reals.Jindřich Zapletal - 2000 - Journal of Symbolic Logic 65 (2):747-755.
    The relationship between killing ideals and adding reals by forcings is analysed.
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  20.  9
    Regular Embeddings of the Stationary Tower and Woodin's Σ 2 2 Maximality Theorem.Richard Ketchersid, Paul B. Larson & Jindřich Zapletal - 2010 - Journal of Symbolic Logic 75 (2):711-727.
    We present Woodin's proof that if there exists a measurable Woodin cardinal δ, then there is a forcing extension satisfying all $\Sigma _{2}^{2}$ sentences ϕ such that CH + ϕ holds in a forcing extension of V by a partial order in V δ . We also use some of the techniques from this proof to show that if there exists a stationary limit of stationary limits of Woodin cardinals, then in a homogeneous forcing extension there is an elementary embedding (...)
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  21.  6
    University of California, San Diego, March 20–23, 1999.Julia F. Knight, Steffen Lempp, Toniann Pitassi, Hans Schoutens, Simon Thomas, Victor Vianu & Jindrich Zapletal - 1999 - Bulletin of Symbolic Logic 5 (3).
  22.  8
    Separation Problems and Forcing.Jindřich Zapletal - 2013 - Journal of Mathematical Logic 13 (1):1350002.
    Certain separation problems in descriptive set theory correspond to a forcing preservation property, with a fusion type infinite game associated to it. As an application, it is consistent with the axioms of set theory that the circle.
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  23. Stanford University, Stanford, CA March 19–22, 2005.Steve Awodey, Raf Cluckers, Ilijas Farah, Solomon Feferman, Deirdre Haskell, Andrey Morozov, Vladimir Pestov, Andre Scedrov, Andreas Weiermann & Jindrich Zapletal - 2006 - Bulletin of Symbolic Logic 12 (1).
     
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  24.  4
    Terminal Notions.Jindřich Zapletal - 1999 - Bulletin of Symbolic Logic 5 (4):470-478.
    Certain set theoretical notions cannot be split into finer subnotions.
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  25.  3
    Why Y-C.C.David Chodounský & Jindřich Zapletal - 2015 - Annals of Pure and Applied Logic 166 (11):1123-1149.
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  26.  3
    2005 Annual Meeting of the Association for Symbolic Logic.Ilijas Farah, Deirdre Haskell, Andrey Morozov, Vladimir Pestov & Jindrich Zapletal - 2006 - Bulletin of Symbolic Logic 12 (1):143.
  27.  3
    Preserving $Sigma$-Ideals.Jindrich Zapletal - 1998 - Journal of Symbolic Logic 63 (4):1437-1441.
    It is proved consistent that there be a proper $\sigma$-ideal $\Im$ on $\omega_1$ and an $\aleph_1$-preserving poset $\mathbb{P}$ such that $\mathbb{P} \Vdash$ the $\sigma$-ideal generated by $\check{\Im}$ is not proper.
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  28.  4
    Terminal Notions in Set Theory.Jindřich Zapletal - 2001 - Annals of Pure and Applied Logic 109 (1-2):89-116.
    In mathematical practice certain formulas φ are believed to essentially decide all other natural properties of the object x. The purpose of this paper is to exactly quantify such a belief for four formulas φ, namely “x is a Ramsey ultrafilter”, “x is a free Souslin tree”, “x is an extendible strong Lusin set” and “x is a good diamond sequence”.
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