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

David Chodounský, Osvaldo Guzmán, Michael Hrušák

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-…