THREE RED HERRINGS AROUND VAUGHT'S CONJECTURE

被引：12

作者：

Baldwin, John T. ^{[1
]}

Koerwien, Sy D. Friedman Martin

Laskowski, Michael C.

机构：

[1] Univ Illinois, Dept Math Stat & Comp Sci, 851 S Morgan St M-C 249, Chicago, IL 60607 USA

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 368卷 / 05期

基金：

奥地利科学基金会;

关键词：

ATOMIC MODELS; CATEGORICITY; CARDINALS;

D O I：

10.1090/tran/6572

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a model theoretic proof that if there is a counterexample to Vaught's conjecture there is a counterexample such that every model of cardinality aleph(1) is maximal (strengthening a result of Hjorth's). In the process we analyze three examples of a sentence characterizing aleph(1). We also give a new proof of Harrington's theorem that any counterexample to Vaught's conjecture has models in aleph(1) of arbitrarily high Scott rank below aleph(2).

引用

页码：3673 / 3694

页数：22

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