arXiv subjects

David Chodounský

Publications and source records attributed to David Chodounský.

22 records · Page 2Linked to original sources

arXiv2016

Mathias--Prikry and Laver type forcing; Summable ideals, coideals, and $+$-selective filters

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 always adds a dominating real. We also characterize filters for which the associated Mathias--Prikry forcing does not add eventually different reals, and show that they are countably generated provided they are Borel. We give a characterization of $ω$-hitting and $ω$-splitting families which retain their property in the extension by a Laver type forcing associated with a coideal.

math.LO↗

arXiv2015

Why Y-c.c

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 partition-type forcings and anticliques in open graphs. Using Neeman's side condition method it is possible to obtain PFA variations and prove consistency results for them.

math.LO↗

arXiv2015

Mathias forcing and combinatorial covering properties of filters

We give topological characterizations of filters $F$ on $w$ such that the Mathias forcing $M_F$ adds no dominating reals or preserves ground model unbounded families. This allows us to answer some questions of Brendle, Guzmán, Hrušák, Mart\'ınez, Minami, and Tsaban.

math.LO↗

arXiv2014

Hausdorff gaps and towers in P(ω)/Fin

We define and study two classes of uncountable $\subseteq^*$-chains: Hausdorff towers and Suslin towers. We discuss their existence in various models of set theory. Then, some of the results and methods are used to provide examples of indestructible gaps not equivalent to a Hausdorff gap. Also, we indicate possible ways of developing a structure theory for towers.

math.LO↗