Selected preprints and publications of Ilijas Farah

  1. The extender algebra and Sigma-2-1 absoluteness, version od December 2009.
     pdf file
  2. A dichotomy for the number of ultrapowers, (joint with Saharon Shelah), December 2009.
    pdf file
  3. Graphs and CCR algebras, to appear in Indiana University Mathematics Journal.
    pdf file
  4. Model theory of operator algebras I: Stability, (joint with Bradd Hart and David Sherman) August 2009.
    pdf file
  5. A dichotomy for the Mackey Borel structure, to appear in Proceedings of the Asian Logic Colloquium 2009. Version of January 2009.
    pdf file
  6. Nonseparable UHF algebras I: Dixmier's problem (joint with Takeshi Katsura), June 2009..
    pdf file
  7. The relative commutant of separable C*-algebras of real rank zero, Journal of Functional Analysis, 256 (2009), no. 11, 3841-3846.
    dvi file pdf file
  8. The commutant of L(H) in its ultrapower may or may not be trivial (joint with N. Christopher Phillips and Juris Steprans), to appear in Math. Annalen.
    pdf file
  9. All automorphisms of the Calkin algebra are inner, March 2007. A revised version of September 29, 2009.
    The proof in Section 3 is fixed, and the proof of Theorem 5.1 is completely rewritten.
    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.

  10. Nonhomogeneity in products of beta-N spaces, Topology and its applications 155 (2008) 273-276.
    dvi file postscript file pdf file
  11. Extreme amenability of L_0, a Ramsey theorem, and Levy groups, (with Slawek Solecki),
    Journal of Functional Analysis. (255) (2008) 471-493.
    dvi file pdf file
  12. Maharam algebras and Cohen reals, (with Boban Velickovic)
    Proceedings of the American Mathematical Society    , 135 (2007) 2283-2290.
    dvi file postscript file pdf file
  13. The fourth head of beta-N. Open Problems in Topology II, E.M. Pearl, ed., Elsevier, 2007, 135-140.
    postscript file dvi file pdf file
  14. Absoluteness for universally Baire sets and the uncountable II, (joint with Richard Ketchersid , Paul B. Larson and Menachem Magidor) 163-191.
    postscript file dvi file pdf file
  15. 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
  16. 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
    . postscript file dvi file pdf file
  17. Von Neumann's problem and large cardinals, (joint with Boban Velickovic) Bulletin of the London Math. Soc. 38 (2006) 907-912.
    dvi file postscript file pdf file
  18. A countable dense homogeneous set of size aleph_1 (with Michael Hrusak and Carlos Azarel Martinez Ranero), Fundamenta Mathematicae186 (2005), 71-77.
    dvi file postscript file pdf file
  19. Four and more, Annals of Pure and Applied Logic 140 (2006), 3-39 (joint with Jindra Zapletal).
    dvi file postscript file
  20. Analytic Hausdorff gaps II: the density zero ideal, Israel Journal of Mathematics 154 (2006) 235-246.
    dvi file postscript file pdf file
  21. Between Maharam's and von Neumann's problems, (joint with Jindra Zapletal) Mathematics Research Letters, 11 (2004), no. 5-6, 673-684.
    dvi file postscript file pdf file
  22. Examples of epsilon-exhaustive submeasures, Fundamenta Mathematicae 181 (2004), 257-272.
    dvi file postscript file pdf file
  23. Borel subgroups of Polish groups. (joint with Slawek Solecki) Advances in Mathematics, 199 (2006), 499-541.
    dvi file postscript file pdf file
  24. Is P(omega) a subalgebra? (joint with Alan Dow). Fundamenta Mathematicae, 183 (2004), 91-108.
    dvi file postscript file pdf file
  25. Luzin gaps, Trans. Amer. Math. Soc. 356 (2004), 2197-2239.
    dvi file postscript file pdf file
  26. Reductions between meager ideals, Fundamentalnaya i Prikladnaya Matematika 11 (2005), 213-219.
    postscript file dvi file pdf file
    (Russian translation available here.)
  27. Two F-sigma-delta ideals, (with Slawek Solecki), Proceedings of the American Mathematical Society 131 (2003), 1971-1975.
    dvi file postscript file pdf file
  28. How many Boolean algebras P(N)/I are there?, Illinois Journal of Mathematics 46 (2003), 999-1033.
    dvi file postscript file pdf file
  29. Analytic Hausdorff gaps, DIMACS Series, 58 (2002), 65-72.
    dvi file postscript file pdf file
  30. 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.
    postscript file dvi file pdf file
  31. Powers of N*, Proceedings of the American Mathematical Society, 130 (2002), 1243-1246.
    postscript file dvi file pdf file
  32. Partition theorems for layered partial semigroups, (with Neil Hindman and Jillian McLeod) Journal of Combinatorial Theory, Ser. A, 98 (2002), 268-311.
    postscript file dvi file pdf file
  33. Dimension phenomena associated with beta-N spaces, Topology and its Applications, 125 (2002), 279-297.
    postscript file dvi file pdf file
  34. Functions essentially depending on at most one variable, Journal of Combinatorial Theory, Ser. A, 94 (2001), 169-177.
    postscript file dvi file pdf file
  35. Basis problem for turbulent actions II: C_0-equalities, Proceedings of the London Mathematical Society, 82 (2001), 1--30.
    postscript file dvi file pdf file
  36. Basis problem for turbulent actions I: Tsirelson submeasures Annals of Pure and Applied Logic (Proceedings of XI SLALM) 108 (2001), 189-203
    postscript file dvi file pdf file
  37. Approximate homomorphisms II: Group homomorphisms, Combinatorica 20, (2000), 47-60.
    postscript file pdf file
  38. 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.

  39. 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
  40. Ideals induced by Tsirelson submeasures , Fundamenta Mathematicae, 159, (1999) 243-258.
    postscript file dvi file pdf file
  41. Cauchy nets and open colorings, Publications de l'Institut Mathematique, 64 (1998), 146-152.
    postscript file dvi file pdf file
  42. Approximate homomorphisms, Combinatorica, 18, (1998), 335-348.
    postscript file dvi file pdf file
  43. Semiselective coideals, Mathematika, 45, (1998), 79-103.
    postscript file dvi file pdf file
  44. Completely additive liftings, The Bulletin of Symbolic Logic, 4, (1998), 37-54.
    postscript file pdf file
  45. OCA and towers in P(N)/fin, Commentationes Mathematicae Universitatis Carolinae, 37, (1996), 861-866.
  46. Embedding partially ordered sets into omega^omega, Fundamenta Mathematicae, 151, (1996), 53-95.
  47. A coherent family of partial functions on N, Proceedings of the American Mathematical Society 124, (1996), 2845-2852.
  48. Some Applications of the Method of Forcing, Yenisei, Moscow (1995) (146 p.) (coauthored with Stevo Todorcevic)

Home