# Existentially closed II₁ factors

Ilijas Farah; Isaac Goldbring; Bradd Hart; David Sherman

Fundamenta Mathematicae (2016)

- Volume: 233, Issue: 2, page 173-196
- ISSN: 0016-2736

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topIlijas Farah, et al. "Existentially closed II₁ factors." Fundamenta Mathematicae 233.2 (2016): 173-196. <http://eudml.org/doc/281668>.

@article{IlijasFarah2016,

abstract = {We examine the properties of existentially closed ($ ^\{ω\}$-embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ($ ^\{ω\}$-embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() 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().},

author = {Ilijas Farah, Isaac Goldbring, Bradd Hart, David Sherman},

journal = {Fundamenta Mathematicae},

keywords = {existentially closed; II1factor; continuous model theory},

language = {eng},

number = {2},

pages = {173-196},

title = {Existentially closed II₁ factors},

url = {http://eudml.org/doc/281668},

volume = {233},

year = {2016},

}

TY - JOUR

AU - Ilijas Farah

AU - Isaac Goldbring

AU - Bradd Hart

AU - David Sherman

TI - Existentially closed II₁ factors

JO - Fundamenta Mathematicae

PY - 2016

VL - 233

IS - 2

SP - 173

EP - 196

AB - We examine the properties of existentially closed ($ ^{ω}$-embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ($ ^{ω}$-embeddable) II₁ factor is approximately inner to prove that Th() is not model-complete. We also show that Th() 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().

LA - eng

KW - existentially closed; II1factor; continuous model theory

UR - http://eudml.org/doc/281668

ER -

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