Universal graphs at the successor of a singular cardinal

被引：16

作者：

Dzamonja, M ^{[1
]}

Shelah, S

机构：

[1] Univ E Anglia, Sch Math, Norwich NR4 7TJ, Norfolk, England

[2] Hebrew Univ Jerusalem, Inst Math, IL-91904 Givat Ram, Israel

[3] Rutgers State Univ, New Brunswick, NJ 08903 USA

来源：

JOURNAL OF SYMBOLIC LOGIC | 2003年 / 68卷 / 02期

关键词：

successor of singular; iterated forcing; universal graph;

D O I：

10.2178/jsl/1052669056

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The paper is concerned with the existence of a universal graph at the successor of a strong limit singular mu of colinality N-0. Starting from the assumption of the existence of a supercompact cardinal, a model is built in which for some such mu there are mu(++) graphs on mu(+) that taken jointly are universal for the graphs on mu(+), while 2mu(+) much greater than u(++). The paper also addresses the general problem of obtaining a framework for consistency results at the successor of a singular strong limit starting from the assumption that a supercompact cardinal kappa exists. The result on the existence of universal graphs is obtained as a specific application of a more general method.

引用

页码：366 / 388

页数：23