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  1. Hypergraphs and proper forcing.Jindřich Zapletal - 2019 - Journal of Mathematical Logic 19 (2):1950007.
    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 the quotient posets are proper. I investigate the forcing properties of these posets, certain natural operations on them, and prove some related dichotomies.
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  • Two chain conditions and their Todorčević's fragments of Martin's Axiom.Teruyuki Yorioka - 2024 - Annals of Pure and Applied Logic 175 (1):103320.
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  • A note on a forcing related to the S‐space problem in the extension with a coherent Suslin tree.Teruyuki Yorioka - 2015 - Mathematical Logic Quarterly 61 (3):169-178.
    One of the main problems about is that whether a coherent Suslin tree forces that there are no S‐spaces under. We analyze a forcing notion related to this problem, and show that under, S forces that every topology on ω1 generated by a basis in the ground model is not an S‐topology. This supplements the previous work due to Stevo Todorčević [25].
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  • P-ideal dichotomy and weak squares.Dilip Raghavan - 2013 - Journal of Symbolic Logic 78 (1):157-167.
    We answer a question of Cummings and Magidor by proving that the P-ideal dichotomy of Todorčević refutes ${\square}_{\kappa, \omega}$ for any uncountable $\kappa$. We also show that the P-ideal dichotomy implies the failure of ${\square}_{\kappa, < \mathfrak{b}}$ provided that $cf(\kappa) > {\omega}_{1}$.
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  • Why Y-c.c.David Chodounský & Jindřich Zapletal - 2015 - Annals of Pure and Applied Logic 166 (11):1123-1149.
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