II1 FACTORS WITH NONISOMORPHIC ULTRAPOWERS

被引：19

作者：

Boutonnet, Remi ^{[1
]}

Chifan, Ionut ^{[2
]}

Ioana, Adrian ^{[3
,4
]}

机构：

[1] Univ Bordeaux 1, CNRS, Inst Math Bordeaux, Talence, France

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[3] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[4] Romanian Acad IMAR, Inst Math, Bucharest, Romania

来源：

DUKE MATHEMATICAL JOURNAL | 2017年 / 166卷 / 11期

基金：

美国国家科学基金会;

关键词：

VON-NEUMANN-ALGEBRAS; MODEL-THEORY; ELEMENTARY EQUIVALENCE; TYPE-2(I) FACTORS; INFINITY;

D O I：

10.1215/00127094-0000017X

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that there exist uncountably many, separable II1,factors whose ultrapowers (with respect,to arbitrary ultrafilters) are nonisomorphic. In fact, we prove that the families of nonisomorphic II1 factors originally introduced by McDuff are such examples. This entails the existence of a continuum of nonelementarily equivalent II1 factors, thus settling a well-known open problem in the continuous model theory of operator algebras.

引用

页码：2023 / 2051

页数：29

共 30 条

[11] GAMES AND ELEMENTARY EQUIVALENCE OF II1-FACTORS [J].

Goldbring, Isaac ;

Sinclair, Thomas .

PACIFIC JOURNAL OF MATHEMATICS, 2015, 278 (01) :103-118

[12]

Jiang XH, 1999, AM J MATH, V121, P359

[13]

Keisler H.J., 1961, Indag. Math., V23, P477

[14]

Keisler HJ, 2010, CONTEMP MATH, V530, P163

[15]

MCDUFF D, 1970, P LOND MATH SOC, V21, P443

[16] UNCOUNTABLY MANY II1 FACTORS [J].

MCDUFF, D .

ANNALS OF MATHEMATICS, 1969, 90 (02) :372-&

[17] A COUNTABLE INFINITY OF II1 FACTORS [J].

MCDUFF, D .

ANNALS OF MATHEMATICS, 1969, 90 (02) :361-+

[18] On rings of operators. IV [J].

Murray, FJ ;

von Neumann, J .

ANNALS OF MATHEMATICS, 1943, 44 :716-808

[19]

Neumann John von, 1942, PORT MATH, V3, P1

[20]

Ozawa N., 2013, Journal of Mathematical Sciences The University of Tokyo, V20, P349

← 1 2 3 →