Different cofinalities of tree ideals

被引：0

作者：

Shelah, Saharon ^{[1
,2
]}

Spinas, Otmar ^{[3
]}

机构：

[1] Hebrew Univ Jerusalem, Einstein Inst Math, Givat Ram, Edmond J Safra Campus, IL-91904 Jerusalem, Israel

[2] Rutgers State Univ, Dept Math, Hill Ctr Busch Campus,110 Frelinghuysen Rd, Piscataway, NJ 08854 USA

[3] Christian Albrechts Univ Kiel, Math Seminar, Ludewig Meyn Str 4, D-24118 Kiel, Germany

来源：

ANNALS OF PURE AND APPLIED LOGIC | 2023年 / 174卷 / 08期

基金：

欧洲研究理事会;

关键词：

Tree forcing; Tree ideal; Additivity; Cofinality;

D O I：

10.1016/j.apal.2023.103290

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a general framework of generalized tree forcings, GTF for short, that includes the classical tree forcings like Sacks, Silver, Laver or Miller forcing. Using this concept we study the cofinality of the ideal I(Q) associated with a GTF Q. We show that if for two GTF's Q0 and Q1 the consistency of add(I(Q0)) < add(I(Q1)) holds, then we can obtain the consistency of cof(I(Q1)) < cof(I(Q0)). We also show that cof(I(Q)) can consistently be any cardinal of cofinality larger than the continuum. (c) 2023 Elsevier B.V. All rights reserved.

引用

页数：18

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