Selected preprints and publications of Ilijas Farah
See also
ResearchGate
and Google Scholar

Logic and operator algebras. To appear in Proceedings of the ICM.
Version of June 2014.

Rigidity of continuous quotients
(joint
with Saharon Shelah),
to appear in J. Math. Inst. Jussieu. Version of June 2014.

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.

Traces, ultrapowers, and the PedersenPetersen C*algebras (joint with
Tristan Bice ),
to appear in Houston Journal of Math. Version of August 2013.

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, 10711080.

A simple C*algebra with finite nuclear dimension
which is not Zstable, (joint with
Dan Hathaway,
Aaron Tikuisis and
Takeshi Katsura),
January 2013. To appear in Munster Journal of Mathematics.
.

Nonseparable UHF algebras II: Classification,
(with Takeshi Katsura), to appear in Math. Scand.
version of July 2013.

Omitting types and AF algebras, joint with
Kevin Carlson, Enoch Cheung, Alexander GerhardtBourke, Bradd Hart, Leanne Mezuman, Nigel Sequeira, and Alexander Sherman,
Archive for Mathematical Logic 53 (2014), 157169.

Independence of the existence of Pitowsky spin models, joint with
Menachem Magidor, December 2012.

Some Calkin algebras have outer automorphisms, joint with Paul McKenney
and Ernest Schimmerling,
Arch. Math. Logic 52 (2013), 517524.

Homeomorphisms of CechStone remainders: the zerodimensional case, joint
with Paul McKenney, November 2012.

Absoluteness, truth, and quotients,
to appear in Proceedings of the IMS Workshop
on Infinity and Truth, C.T. Chong et al, editors
, World Scientific, 124.

Selected applications of logic to classification problem of C*algebras,
(notes from Singapore summer school),
In: Erecursion, forcing and C*algebras, C.T. Chong et al, eds., World Scientific, 2014, 183.

Automorphisms of corona algebras, and group cohomology
(joint with Sam Coskey), April 2012.
Trans. Amer. Math. Soc. 366 (2014), no. 7, 36113630.
 Countable saturation of corona algebras,
(joint with Bradd Hart)
C. R. Math. Rep. Acad. Sci. Canada Vol. 35 (2) 2013, pp. 3556.
 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) 51965226
,
 Trivial automorphisms
(joint
with Saharon Shelah),
Israel J. Math 201 (2014) 701728.
 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)
120.
 Turbulence, orbit equivalence, and the classification of nuclear C*algebras
(with Andrew S. Toms
and Asger Tornquist,
Journal fŸr die reine und angewandte Mathematik (Crelles Journal),
688 (2014) 101146.

All automorphisms of all Calkin algebras, Math. Res. Letters,
18 (2011), 489503.
 Set theory and operator algebras (with Eric Wofsey),
Appalachian Set Theory: 20062012,
(James Cummings
and Ernest Schimmerling, editors),
London Math. Soc. Lecture Note Series 406 (2012), 63120.
 Model theory of operator algebras II: Model theory,
(joint with Bradd Hart
and David Sherman)
Israel J. Math. 201 (2014) 477505.
 The extender algebra and Sigma21 absoluteness,
version of November 2011, to appear in The Cabal Seminar, vol. 4
(Alexander
S. Kechris ,
Benedikt Loewe ,
John R. Steel, editors).
 A dichotomy for the number of ultrapowers, (joint
with Saharon Shelah),
Journal of Mathematical Logic
10,
(2010),
4581.
 Graphs and CCR algebras,
Indiana Univ. Math. J. 59 No. 3 (2010), 1041Ð1056.
 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.
 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
8693 (2011).
 Nonseparable UHF algebras I: Dixmier's problem (joint with Takeshi Katsura), Advances in Math. 225 (2010) 13991430.
 The relative commutant of separable C*algebras of real rank zero, Journal of Functional Analysis, 256 (2009), no. 11, 38413846.
 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), 839857.
 All automorphisms of the Calkin algebra are inner,
Annals of Mathematics 173 (2011), 619Ð661.
The slides from my tutorial on automorphisms of the Calkin algebra at the Luminy set theory workshop, September 2226, 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.
 Nonhomogeneity in products of betaN spaces,
Topology and its applications 155 (2008) 273276.
 Extreme amenability of L_0,
a Ramsey theorem,
and Levy groups,
(with Slawek Solecki),
Journal of Functional Analysis. (255) (2008) 471493.
 Maharam algebras and Cohen reals,
(with
Boban Velickovic)
Proceedings of the American Mathematical
Society, 135 (2007) 22832290.
 The fourth head of betaN. Open Problems in Topology II, E.M. Pearl, ed., Elsevier, 2007, 135140.
 Absoluteness for universally Baire sets and the uncountable II, (joint with
Richard Ketchersid ,
Paul B. Larson and
Menachem Magidor) 163191.
 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., 4792.

A proof of the Sigma21 absoluteness theorem. Advances in Logic, S. Gao, S. Jackson and Y. Zhang, eds.,
Contemporary Mathematics,
425 (2007) American Mathematical Society, RI., 922
.
 Von Neumann's problem and large cardinals,
(joint with
Boban Velickovic)
Bulletin of the London Math. Soc. 38 (2006) 907912.
 A countable dense homogeneous set of size aleph_1
(with
Michael Hrusak and Carlos Azarel Martinez Ranero), Fundamenta
Mathematicae186 (2005), 7177.
 Four and more,
Annals of Pure and Applied Logic
140 (2006), 339 (joint with Jindra Zapletal).
 Analytic Hausdorff gaps II: the density zero ideal,
Israel Journal of Mathematics 154 (2006) 235246.
 Between Maharam's and von Neumann's problems,
(joint with Jindra Zapletal)
Mathematics
Research Letters,
11 (2004), no. 56, 673684.
 Examples of epsilonexhaustive submeasures,
Fundamenta
Mathematicae 181 (2004), 257272.
 Borel subgroups of Polish groups.
(joint with Slawek Solecki)
Advances in Mathematics, 199 (2006), 499541.
 Is P(omega) a subalgebra?
(joint with Alan Dow).
Fundamenta
Mathematicae, 183 (2004), 91108.
 Luzin gaps,
Trans. Amer. Math. Soc.
356
(2004), 21972239.

Reductions between meager ideals, Fundamentalnaya i Prikladnaya Matematika 11 (2005), 213219.
(Russian translation available here.)

Two Fsigmadelta ideals, (with Slawek
Solecki),
Proceedings of the American Mathematical
Society 131 (2003), 19711975.
 How many Boolean algebras P(N)/I are there?,
Illinois Journal of Mathematics 46 (2003), 9991033.

Analytic Hausdorff gaps, DIMACS Series, 58
(2002), 6572.

Rigidity conjectures, (a survey of new developments since
Analytic quotients was completed. In: Proceedings
of Logic Colloquium 2000, R. Cori et al., editors. (2005), 252271.

Powers of N*,
Proceedings of the American Mathematical
Society, 130 (2002), 12431246.

Partition theorems for layered partial semigroups,
(with Neil Hindman
and Jillian McLeod)
Journal of Combinatorial Theory,
Ser. A, 98 (2002), 268311.

Dimension phenomena associated with
betaN spaces,
Topology and its Applications, 125 (2002), 279297.

Functions essentially depending on at most one variable,
Journal of Combinatorial Theory,
Ser. A, 94 (2001), 169177.

Basis problem for turbulent actions II: C_0equalities,
Proceedings of the London Mathematical
Society, 82 (2001), 130.
 Basis problem for turbulent actions I: Tsirelson submeasures
Annals of Pure and Applied Logic (Proceedings of XI SLALM) 108 (2001), 189203

Approximate homomorphisms II: Group
homomorphisms,
Combinatorica
20, (2000), 4760.

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.

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), 173196.
 Ideals induced by Tsirelson submeasures ,
Fundamenta
Mathematicae,
159, (1999) 243258.
 Cauchy nets and open colorings,
Publications
de l'Institut Mathematique,
64 (1998), 146152.
 Approximate homomorphisms,
Combinatorica,
18, (1998), 335348.
 Semiselective coideals,
Mathematika, 45, (1998), 79103.
 Completely additive liftings,
The
Bulletin of Symbolic Logic, 4, (1998), 3754.
 OCA and towers in P(N)/fin,
Commentationes Mathematicae Universitatis Carolinae, 37, (1996), 861866.
 Embedding partially ordered sets into omega^omega,
Fundamenta
Mathematicae, 151, (1996), 5395.
 A coherent family of partial functions on N,
Proceedings of the American Mathematical
Society 124, (1996),
28452852.
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