David Chodounský

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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 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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