Geodesic
Existentially closed ${\rm II}_1$ factors
Ilijas Farah 1   ; Isaac Goldbring 2   ; Bradd Hart 3   ; David Sherman 4
1 Department of Mathematics and Statistics York University 4700 Keele Street York, Ontario, Canada, M3J 1P3 <a href="http://www.math.yorku.ca/~ifarah">URL: http://www.math.yorku.ca/~ifarah</a>
2 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. <a href="http://www.math.uic.edu/~isaac">URL: http://www.math.uic.edu/~isaac</a>
3 Department of Mathematics and Statistics McMaster University 1280 Main Street W. Hamilton, Ontario, Canada L8S 4K1 <a href="http://www.math.mcmaster.ca/~bradd">URL: http://www.math.mcmaster.ca/~bradd</a>
4 Department of Mathematics University of Virginia P.O. Box 400137 Charlottesville, VA 22904-4137, U.S.A. <a href="http://people.virginia.edu/~des5e">URL: http://people.virginia.edu/~des5e</a>
Fundamenta Mathematicae, Tome 233 (2016) no. 2, pp. 173-196 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We examine the properties of existentially closed ($\mathcal {R}^\omega $-embeddable) ${\rm II}_1$ factors. In particular, we use the fact that every automorphism of an existentially closed ($\mathcal {R}^\omega $-embeddable) ${\rm II}_1$ factor is approximately inner to prove that $\operatorname {Th}(\mathcal {R})$ is not model-complete. We also show that $\operatorname {Th}(\mathcal {R})$ 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 $\operatorname {Th}(\mathcal {R})$.
DOI : 10.4064/fm126-12-2015
Keywords: examine properties existentially closed mathcal omega embeddable factors particular every automorphism existentially closed mathcal omega embeddable factor approximately inner prove operatorname mathcal model complete operatorname mathcal complete finite infinite forcing latter result prove there exist continuum many nonisomorphic existentially closed models operatorname mathcal

Ilijas Farah  1   ; Isaac Goldbring  2   ; Bradd Hart  3   ; David Sherman  4

1 Department of Mathematics and Statistics York University 4700 Keele Street York, Ontario, Canada, M3J 1P3 <a href="http://www.math.yorku.ca/~ifarah">URL: http://www.math.yorku.ca/~ifarah</a>
2 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. <a href="http://www.math.uic.edu/~isaac">URL: http://www.math.uic.edu/~isaac</a>
3 Department of Mathematics and Statistics McMaster University 1280 Main Street W. Hamilton, Ontario, Canada L8S 4K1 <a href="http://www.math.mcmaster.ca/~bradd">URL: http://www.math.mcmaster.ca/~bradd</a>
4 Department of Mathematics University of Virginia P.O. Box 400137 Charlottesville, VA 22904-4137, U.S.A. <a href="http://people.virginia.edu/~des5e">URL: http://people.virginia.edu/~des5e</a> 
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     title = {Existentially closed ${\rm II}_1$ factors},
     journal = {Fundamenta Mathematicae},
     pages = {173--196},
     year = {2016},
     volume = {233},
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     doi = {10.4064/fm126-12-2015},
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Ilijas Farah; Isaac Goldbring; Bradd Hart; David Sherman. Existentially closed ${\rm II}_1$ factors. Fundamenta Mathematicae, Tome 233 (2016) no. 2, pp. 173-196. doi: 10.4064/fm126-12-2015

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