Selected preprints and publications of Ilijas Farah

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  1. Logic and operator algebras. To appear in Proceedings of the ICM. Version of June 2014.
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  2. Rigidity of continuous quotients (joint with Saharon Shelah), to appear in J. Math. Inst. Jussieu. Version of June 2014.
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  3. A nonseparable amenable operator algebra which is not isomorphic to a C*-algebra (joint with Yemon Choi and Taka Ozawa ), Version of November 2013. To appear in Forum of Mathematics Sigma.
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  4. Traces, ultrapowers, and the Pedersen-Petersen C*-algebras (joint with Tristan Bice ), to appear in Houston Journal of Math. Version of August 2013.
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  5. The isomorphism relation for separable C*-algebras, (joint with George A. Elliott, Vern Paulsen, Christian Rosendal, Andrew S. Toms and Asger Tornquist), Math. Res. Lett. 20 (2013), no. 6, 1071-1080.
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  6. A simple C*-algebra with finite nuclear dimension which is not Z-stable, (joint with Dan Hathaway, Aaron Tikuisis and Takeshi Katsura), January 2013. To appear in Munster Journal of Mathematics.
    pdf file.
  7. Nonseparable UHF algebras II: Classification, (with Takeshi Katsura), to appear in Math. Scand. version of July 2013.
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  8. Omitting types and AF algebras, joint with Kevin Carlson, Enoch Cheung, Alexander Gerhardt-Bourke, Bradd Hart, Leanne Mezuman, Nigel Sequeira, and Alexander Sherman, Archive for Mathematical Logic 53 (2014), 157-169.
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  9. Independence of the existence of Pitowsky spin models, joint with Menachem Magidor, December 2012.
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  10. Some Calkin algebras have outer automorphisms, joint with Paul McKenney and Ernest Schimmerling, Arch. Math. Logic 52 (2013), 517-524.
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  11. Homeomorphisms of Cech-Stone remainders: the zero-dimensional case, joint with Paul McKenney, November 2012.
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  12. Absoluteness, truth, and quotients, to appear in Proceedings of the IMS Workshop on Infinity and Truth, C.T. Chong et al, editors
    pdf file, World Scientific, 1--24.
  13. Selected applications of logic to classification problem of C*-algebras, (notes from Singapore summer school), In: E-recursion, forcing and C*-algebras, C.T. Chong et al, eds., World Scientific, 2014, 1-83.
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  14. Automorphisms of corona algebras, and group cohomology (joint with Sam Coskey), April 2012. Trans. Amer. Math. Soc. 366 (2014), no. 7, 3611-3630.
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  15. Countable saturation of corona algebras, (joint with Bradd Hart) C. R. Math. Rep. Acad. Sci. Canada Vol. 35 (2) 2013, pp. 35-56.
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  16. The descriptive set theory of C*-algebra invariants, (with Andrew S. Toms and Asger Tornquist and appendix with Caleb Eckhardt, Int. Math. Res. Notices 22 (2013) 5196--5226 ,
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  17. Trivial automorphisms (joint with Saharon Shelah), Israel J. Math 201 (2014) 701-728.
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  18. Model theory of operator algebras III: Elementary equivalence and II_1 factors, (joint with Bradd Hart and David Sherman) Bull. London Math. Soc. 46 (2014) 1-20.
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  19. Turbulence, orbit equivalence, and the classification of nuclear C*-algebras (with Andrew S. Toms and Asger Tornquist, Journal fr die reine und angewandte Mathematik (Crelles Journal), 688 (2014) 101-146.
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  20. All automorphisms of all Calkin algebras, Math. Res. Letters, 18 (2011), 489-503.
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  21. Set theory and operator algebras (with Eric Wofsey), Appalachian Set Theory: 2006-2012, (James Cummings and Ernest Schimmerling, editors), London Math. Soc. Lecture Note Series 406 (2012), 63-120.
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  22. Model theory of operator algebras II: Model theory, (joint with Bradd Hart and David Sherman) Israel J. Math. 201 (2014) 477-505.
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  23. The extender algebra and Sigma-2-1 absoluteness, version of November 2011, to appear in The Cabal Seminar, vol. 4 (Alexander S. Kechris , Benedikt Loewe , John R. Steel, editors).
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  24. A dichotomy for the number of ultrapowers, (joint with Saharon Shelah), Journal of Mathematical Logic 10, (2010), 45-81.
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  25. Graphs and CCR algebras, Indiana Univ. Math. J. 59 No. 3 (2010), 10411056.
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  26. Model theory of operator algebras I: Stability, (joint with Bradd Hart and David Sherman, to appear in Bulletin of London Math. Soc.) Version of July 2012.
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  27. A dichotomy for the Mackey Borel structure, Proceedings of the 11th Asian Logic Conference In Honor of Professor Chong Chitat on His 60th Birthday, Yang Yue et. al., editors 86--93 (2011).
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  28. Nonseparable UHF algebras I: Dixmier's problem (joint with Takeshi Katsura), Advances in Math. 225 (2010) 1399-1430.
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  29. The relative commutant of separable C*-algebras of real rank zero, Journal of Functional Analysis, 256 (2009), no. 11, 3841-3846.
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  30. The commutant of L(H) in its ultrapower may or may not be trivial (joint with N. Christopher Phillips and Juris Steprans), Mathematische Annalen, 347 (2010), 839-857.
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  31. All automorphisms of the Calkin algebra are inner, Annals of Mathematics 173 (2011), 619661.
    pdf file
    The slides from my tutorial on automorphisms of the Calkin algebra at the Luminy set theory workshop, September 22-26, 2008, are available here and also in a more compact version They may be used as a guide to the proof. Please note that the terminology used in the talk somewhat differs from that used in the paper. I hope that a slightly different angle may help in understanding the proof.

  32. Nonhomogeneity in products of beta-N spaces, Topology and its applications 155 (2008) 273-276.
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  33. Extreme amenability of L_0, a Ramsey theorem, and Levy groups, (with Slawek Solecki),
    Journal of Functional Analysis. (255) (2008) 471-493.
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  34. Maharam algebras and Cohen reals, (with Boban Velickovic)
    Proceedings of the American Mathematical Society
    , 135 (2007) 2283-2290.
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  35. The fourth head of beta-N. Open Problems in Topology II, E.M. Pearl, ed., Elsevier, 2007, 135-140.
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  36. Absoluteness for universally Baire sets and the uncountable II, (joint with Richard Ketchersid , Paul B. Larson and Menachem Magidor) 163-191.
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  37. Absoluteness for universally Baire sets and the uncountable I. (joint with Paul B. Larson)
    Quaderni di Matematica. 17 (2006) Set Theory: Recent Trends and Applications, A. Andretta, ed., 47-92.
    postscript file dvi file pdf file
  38. A proof of the Sigma-2-1 absoluteness theorem. Advances in Logic, S. Gao, S. Jackson and Y. Zhang, eds., Contemporary Mathematics, 425 (2007) American Mathematical Society, RI., 9-22
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  39. Von Neumann's problem and large cardinals, (joint with Boban Velickovic) Bulletin of the London Math. Soc. 38 (2006) 907-912.
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  40. A countable dense homogeneous set of size aleph_1 (with Michael Hrusak and Carlos Azarel Martinez Ranero), Fundamenta Mathematicae186 (2005), 71-77.
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  41. Four and more, Annals of Pure and Applied Logic 140 (2006), 3-39 (joint with Jindra Zapletal).
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  42. Analytic Hausdorff gaps II: the density zero ideal, Israel Journal of Mathematics 154 (2006) 235-246.
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  43. Between Maharam's and von Neumann's problems, (joint with Jindra Zapletal) Mathematics Research Letters, 11 (2004), no. 5-6, 673-684.
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  44. Examples of epsilon-exhaustive submeasures, Fundamenta Mathematicae 181 (2004), 257-272.
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  45. Borel subgroups of Polish groups. (joint with Slawek Solecki) Advances in Mathematics, 199 (2006), 499-541.
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  46. Is P(omega) a subalgebra? (joint with Alan Dow). Fundamenta Mathematicae, 183 (2004), 91-108.
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  47. Luzin gaps, Trans. Amer. Math. Soc. 356 (2004), 2197-2239.
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  48. Reductions between meager ideals, Fundamentalnaya i Prikladnaya Matematika 11 (2005), 213-219.
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    (Russian translation available here.)
  49. Two F-sigma-delta ideals, (with Slawek Solecki), Proceedings of the American Mathematical Society 131 (2003), 1971-1975.
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  50. How many Boolean algebras P(N)/I are there?, Illinois Journal of Mathematics 46 (2003), 999-1033.
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  51. Analytic Hausdorff gaps, DIMACS Series, 58 (2002), 65-72.
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  52. Rigidity conjectures, (a survey of new developments since Analytic quotients was completed. In: Proceedings of Logic Colloquium 2000, R. Cori et al., editors. (2005), 252--271.
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  53. Powers of N*, Proceedings of the American Mathematical Society, 130 (2002), 1243-1246.
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  54. Partition theorems for layered partial semigroups, (with Neil Hindman and Jillian McLeod) Journal of Combinatorial Theory, Ser. A, 98 (2002), 268-311.
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  55. Dimension phenomena associated with beta-N spaces, Topology and its Applications, 125 (2002), 279-297.
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  56. Functions essentially depending on at most one variable, Journal of Combinatorial Theory, Ser. A, 94 (2001), 169-177.
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  57. Basis problem for turbulent actions II: C_0-equalities, Proceedings of the London Mathematical Society, 82 (2001), 1--30.
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  58. Basis problem for turbulent actions I: Tsirelson submeasures Annals of Pure and Applied Logic (Proceedings of XI SLALM) 108 (2001), 189-203
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  59. Approximate homomorphisms II: Group homomorphisms, Combinatorica 20, (2000), 47-60.
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  60. Analytic quotients: theory of liftings for quotients over analytic ideals on the integers (Memoirs of the American Mathematical Society, 148, No. 702, 177 pp. November 2000)
    Order it here.
    Analytic quotients homepage.


  61. Liftings of homomorphisms between quotient structures and Ulam stability,
    In: S. Buss et. al, editors, Logic Colloquium '98, Lecture notes in logic 13, A.K. Peters, (2000), 173-196.
    postscript file pdf file
  62. Ideals induced by Tsirelson submeasures , Fundamenta Mathematicae, 159, (1999) 243-258.
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  63. Cauchy nets and open colorings, Publications de l'Institut Mathematique, 64 (1998), 146-152.
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  64. Approximate homomorphisms, Combinatorica, 18, (1998), 335-348.
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  65. Semiselective coideals, Mathematika, 45, (1998), 79-103.
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  66. Completely additive liftings, The Bulletin of Symbolic Logic, 4, (1998), 37-54.
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  67. OCA and towers in P(N)/fin, Commentationes Mathematicae Universitatis Carolinae, 37, (1996), 861-866.
  68. Embedding partially ordered sets into omega^omega, Fundamenta Mathematicae, 151, (1996), 53-95.
  69. A coherent family of partial functions on N, Proceedings of the American Mathematical Society 124, (1996), 2845-2852.
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