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  1. Michael Hrušák, Diego Rojas-Rebolledo & Jindřich Zapletal (2014). Cofinalities of Borel Ideals. Mathematical Logic Quarterly 60 (1-2):31-39.
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  2. Jindřich Zapletal (2013). Analytic Equivalence Relations and the Forcing Method. 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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  3. Jindřich Zapletal (2013). Separation Problems and Forcing. Journal of Mathematical Logic 13 (1):1350002.
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  4. Marcin Sabok & Jindřich Zapletal (2011). Forcing Properties of Ideals of Closed Sets. 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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  5. Richard Ketchersid, Paul B. Larson & Jindřich Zapletal (2010). Regular Embeddings of the Stationary Tower and Woodin's Σ 2 2 Maximality Theorem. 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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  6. Jindrich Zapletal (2010). Applications of the Ergodic Iteration Theorem. Mathematical Logic Quarterly 56 (2):116-125.
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  7. Michael Hrušák & Jindřich Zapletal (2008). Forcing with Quotients. 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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  8. Richard Ketchersid, Paul Larson & Jindřich Zapletal (2007). Increasing Δ 1 2 and Namba-Style Forcing. 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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  9. Steve Awodey, Raf Cluckers, Ilijas Farah, Solomon Feferman, Deirdre Haskell, Andrey Morozov, Vladimir Pestov, Andre Scedrov, Andreas Weiermann & Jindrich Zapletal (2006). Stanford University, Stanford, CA March 19–22, 2005. Bulletin of Symbolic Logic 12 (1).
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  10. Ilijas Farah, Deirdre Haskell, Andrey Morozov, Vladimir Pestov & Jindrich Zapletal (2006). 2005 Annual Meeting of the Association for Symbolic Logic. Bulletin of Symbolic Logic 12 (1):143.
     
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  11. Ilijas Farah & Jindřich Zapletal (2006). Four and More. Annals of Pure and Applied Logic 140 (1):3-39.
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  12. Jindřich Zapletal (2003). Isolating Cardinal Invariants. Journal of Mathematical Logic 3 (01):143-162.
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  13. Itay Neeman & Jindřich Zapletal (2001). Proper Forcing and L(ℝ). 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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  14. Jindřich Zapletal (2001). Terminal Notions in Set Theory. Annals of Pure and Applied Logic 109 (1-2):89-116.
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  15. Jindřich Zapletal (2000). Killing Ideals and Adding Reals. Journal of Symbolic Logic 65 (2):747-755.
    The relationship between killing ideals and adding reals by forcings is analysed.
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  16. Julia F. Knight, Steffen Lempp, Toniann Pitassi, Hans Schoutens, Simon Thomas, Victor Vianu & Jindrich Zapletal (1999). University of California, San Diego, March 20–23, 1999. Bulletin of Symbolic Logic 5 (3).
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  17. Saharon Shelah & Jindrich Zapletal (1999). Canonical Models for ℵ1-Combinatorics. Annals of Pure and Applied Logic 98 (1):217-259.
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  18. Jindřich Zapletal (1999). Terminal Notions. Bulletin of Symbolic Logic 5 (4):470-478.
    Certain set theoretical notions cannot be split into finer subnotions.
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  19. Jindřich Zapletal (1998). Preserving Σ-Ideals. 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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  20. Jindrich Zapletal (1998). Preserving $Sigma$-Ideals. 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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  21. Bohuslav Balcar, Thomas Jech & Jindřich Zapletal (1997). Semi-Cohen Boolean Algebras. Annals of Pure and Applied Logic 87 (3):187-208.
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  22. Jindřich Zapletal (1997). Small Forcings and Cohen Reals. 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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  23. Jindřich Zapletal (1997). Splitting Number at Uncountable Cardinals. 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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  24. Jindřich Zapletal (1995). More on the Cut and Choose Game. Annals of Pure and Applied Logic 76 (3):291-301.
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