Categoricity from one successor cardinal in tame abstract elementary classes

被引：39

作者：

Grossberg, Rami ^{[1
]}

Vandieren, Monica

机构：

[1] Carnegie Mellon Univ, Dept Math, Pittsburgh, PA 15213 USA

[2] Robert Morris Univ, Dept Math, Moon Township, PA 15108 USA

来源：

JOURNAL OF MATHEMATICAL LOGIC | 2006年 / 6卷 / 02期

关键词：

model theory; classification theory; abstract elementary classes; stability; categoricity;

D O I：

10.1142/S0219061306000554

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that from categoricity in lambda(+) we can get categoricity in all cardinals >= lambda(+) in a chi-tame abstract elementary classe K which has arbitrarily large models and satisfies the amalgamation and joint embedding properties, provided lambda > LS(K) and lambda >= chi. For the missing case when lambda = LS(K), we prove that K is totally categorical provided that K is categorical in LS(K) and LS(K)(+).

引用

页码：181 / 201

页数：21

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