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- David Chodounský, Dusan Repovs, Lyubomyr Zdomskyy
- J. Symb. Log.
- 2015

- David Chodounský, Jindrich Zapletal
- Ann. Pure Appl. Logic
- 2015

We outline a portfolio of novel iterable properties of c.c.c. and proper forcing notions and study its most important instantiations, Y-c.c. and Y-properness. These properties have interesting consequences for partitiontype forcings and anticliques in open graphs. Using Neeman’s side condition method it is possible to obtain PFA variations and prove… (More)

We give topological characterizations of filters F on ω such that the Mathias forcing MF adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzmán, Hrušák, Mart́ınez, Minami, and Tsaban.

We show that the existence of a homeomorphism between ω∗ 0 and ω∗ 1 entails the existence of a non-trivial autohomeomorphism of ω∗ 0 . This answers Problem 441 in [7]. We also discuss the joint consistency of various consequences of ω∗ 0 and ω∗ 1

- David Chodounský, Osvaldo Guzmán González, Michael Hrusák
- Arch. Math. Log.
- 2016

We study the Mathias–Prikry and the Laver type forcings associated with filters and coideals. We isolate a crucial combinatorial property of Mathias reals, and prove that Mathias–Prikry forcings with summable ideals are all mutually bi-embeddable. We show that Mathias forcing associated with the complement of an analytic ideal does add a dominating real. We… (More)

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