Existentially closed II1 factors

被引：20

作者：

Farah, Ilijas ^{[1
]}

Goldbring, Isaac ^{[2
]}

Hart, Bradd ^{[3
]}

Sherman, David ^{[4
]}

机构：

[1] York Univ, Dept Math & Stat, 4700 Keele St, York, ON M3J 1P3, Canada

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

[3] McMaster Univ, Dept Math & Stat, 1280 Main St W, Hamilton, ON L8S 4K1, Canada

[4] Univ Virginia, Dept Math, POB 400137, Charlottesville, VA 22904 USA

来源：

FUNDAMENTA MATHEMATICAE | 2016年 / 233卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

existentially closed; II1; factor; continuous model theory; MODEL-THEORY; ALGEBRAS;

D O I：

10.4064/fm126-12-2015

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We examine the properties of existentially closed (R-omega-embeddable) factors. In particular, we use the fact that every automorphism of an existentially closed (R-omega-embeddable) II1 factor is approximately inner to prove that Th(R) is not model complete. We also show that Th('R) is complete for both finite and infinite forcing and use the latter result to prove that there exist continuum many nonisomorphic existentially closed models of Th(R).

引用

页码：173 / 196

页数：24

共 19 条

[1] Amenable correspondences and approximation properties for von Neumann algebras [J].