Existentially closed II₁ factors

• Autorzy: Ilijas Farah , Isaac Goldbring , Bradd Hart , David Sherman
• Języki publikacji: EN

Abstrakty

EN

We examine the properties of existentially closed ($𝓡 ^{ω}$-embeddable) II₁ factors. In particular, we use the fact that every automorphism of an existentially closed ($𝓡 ^{ω}$-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).

Kategorie tematyczne

• 03C25: Model-theoretic forcing
• 03C07: Basic properties of first-order languages and structures
• 03C50: Models with special properties (saturated, rigid, etc.)
• 46L36: Classification of factors

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2016
• Tom: 233
• Numer: 2
• Strony: 173-196

Daty

wydano

2016

Twórcy

autor

Ilijas Farah

• Department of Mathematics and Statistics, York University, 4700 Keele Street, York, Ontario, Canada, M3J 1P3

autor

Isaac Goldbring

• Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, Science and Engineering Offices M/C 249, 851 S. Morgan St., Chicago, IL 60607-7045, U.S.A.

autor

Bradd Hart

• Department of Mathematics and Statistics, McMaster University, 1280 Main Street W., Hamilton, Ontario, Canada L8S 4K1

autor

David Sherman

• Department of Mathematics, University of Virginia, P.O. Box 400137, Charlottesville, VA 22904-4137, U.S.A.

Identyfikatory

DOI

10.4064/fm126-12-2015