Mathias-Prikry and Laver type forcing; summable ideals, coideals, and plus -selective filters

被引：6

作者：

Chodounsky, David ^{[1
]}

Guzman Gonzalez, Osvaldo ^{[2
]}

Hrusak, Michael ^{[3
]}

机构：

[1] Acad Sci Czech Republic, Inst Math, Zitna 25, CR-11567 Prague 1, Czech Republic

[2] Univ Nacl Autonoma Mexico, Inst Matemat, Apartado Postal 61-3, Morelia 58089, Michoacan, Mexico

[3] Univ Nacl Autonoma Mexico, Inst Matemat, Area Invest Cient, Circuito Exterior, Ciudad Univ, Mexico City 04510, DF, Mexico

来源：

ARCHIVE FOR MATHEMATICAL LOGIC | 2016年 / 55卷 / 3-4期

关键词：

Mathias-Prikry forcing; Laver type forcing; Mathias like real; +-Selective filter; Dominating real; Eventually different real; omega-Hitting; BOOLEAN-ALGEBRAS;

D O I：

10.1007/s00153-016-0476-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 omega-hitting and omega-splitting families which retain their property in the extension by a Laver type forcing associated with a coideal.

引用

页码：493 / 504

页数：12