@article{adams, 

AUTHOR   = {Adams, Scot}, 

TITLE    = {Indecomposability of treed equivalence relations}, 

JOURNAL  = {The Israel Journal of Mathematics}, 

VOLUME   = {112}, 

YEAR     = {1990}, 

PAGES    = {271-287},

}





@article{adamskechris, 

AUTHOR   = {Adams, Scot and Kechris, Alexander}, 

TITLE    = {Linear algebraic groups and countable {B}orel equivalence relations}, 

JOURNAL  = {The Journal of the American Mathematical 

Society}, 

VOLUME   = {13}, 

YEAR     = {2000}, 

PAGES    = {909-943},

}


@article{anhjne,

AUTHOR   = {Andretta, Alex and Hjorth, Greg and Neeman, Itay},
 
TITLE    = {Effective cardinals in bold faced point classes}, 

JOURNAL  = {preprint}, 

YEAR     = {$\infty$},
}



@incollection{beckercompact,  

AUTHOR   = {Becker, Howard}, 

TITLE    = {The number of path-components of a 

compact subset of $\mathbb{R}^n$}, 

BOOKTITLE = {Logic Colloquim '95},

SERIES    = {Lecture Notes in Logic}, 

VOLUME    = {11}, 

PAGES    = {1-16}, 

PUBLISHER = {Springer}, 

ADDRESS = {Berlin}, 

YEAR    = {1998}

}





@article{beckervaught,

AUTHOR   = {Becker, Howard}, 

TITLE    = {Polish group actions: dichotomies and

generalized embeddings}, 

JOURNAL  = {The Journal of the American Mathematical 

Society}, 

VOLUME   = {11}, 

YEAR     = {1998}, 

PAGES    = {397-449},

}





@book {beckerkechris,

    AUTHOR = {Becker, Howard and Kechris, Alexander},

     TITLE = {The descriptive set theory of {P}olish group actions},

    SERIES = {London Mathematical Society Lecture Note Series},

 PUBLISHER = {Cambridge University Press},

   ADDRESS = {Cambridge},

      YEAR = {1996},

}











@article{burgessselection,  

AUTHOR   = {Burgess, John}, 

TITLE    = {A selection theorem for 

group actions}, 

JOURNAL  = {The Pacific Journal of Mathematics}, 

VOLUME   = {80}, 

YEAR     = {1979}, 

PAGES    = {333-336},

}

@article{gaocamerlo,  

AUTHOR   = {Gao, Su and Camerlo, Riccardo}, 

TITLE    = {The completeness of the isomorphism relation for 
countable Boolean algebras}, 

JOURNAL  = {The Transactions of the American Mathematical 
Society}, 

VOLUME   = {353}, 

YEAR     = {2001}, 

PAGES    = {491-518},

}








@article{cofewe,  

AUTHOR   = {Connes, Alain and Feldman, Jacob and 

Benjamin Weiss}, 

TITLE    = {An amenable equivalence relation is 

generated by a single transformation}, 

JOURNAL  = {The Journal of 
Ergodic Theory and Dynamical Systems}, 

VOLUME   = {1}, 

YEAR     = {1981}, 

PAGES    = {431-450},

}









@article{dokelo,  

AUTHOR   = {Dougherty, Randall and Jackson, Steve and  Kechris, Alexander}, 

TITLE    = {The structure of hyperfinite 

{B}orel equivalence relations}, 

JOURNAL  = {The Transactions of the American Mathematical 

Society}, 

VOLUME   = {341}, 

YEAR     = {1994}, 

PAGES    = {193-225},

}







@article{effros,  

AUTHOR   = {Effros, Edward}, 

TITLE    = {Transformation groups and 

${C}^*$-algebras}, 

JOURNAL  = {The Annals of Mathematics}, 

VOLUME   = {81}, 

YEAR     = {1965}, 

PAGES    = {38-55},

}





 















@article{farahtsirelson,  

AUTHOR   = {Farah, Ilijas}, 

TITLE    = {The basis problem for turbulent actions 

{I}}, 

JOURNAL  = {The Annals of Pure and Applied Logic}, 

VOLUME   = {108}, 

YEAR     = {2001}, 

PAGES    = {189-203},

}









@article{farahdescending,  

AUTHOR   = {Farah, Ilijas}, 

TITLE    = {The basis problem for turbulent 

actions {II}}, 

JOURNAL  = {The Proceedings of the London 

Mathematical Society}, 

VOLUME   = {82}, 

YEAR     = {2001}, 

PAGES    = {169-177},

}







@article{farahmazur,  

AUTHOR   = {Farah, Ilijas}, 

TITLE    = {Ideals induced by {T}sirelson submeasures}, 

JOURNAL  = {Fundamenta Mathematicae}, 

VOLUME   = {159}, 

YEAR     = {1999}, 

PAGES    = {243-259},

}






@article{feldman,

AUTHOR   = {Feldman, Jacob},
 
TITLE    = {Borel structures and invariants for measurable 
transformations},

JOURNAL  = {The Proceedings of the American Mathematical 
Society},

VOLUME   = {46},

YEAR     = {1974},

PAGES    = {383-394},

}






@article{feldmanmoore,  

AUTHOR   = {Feldman, Jacob and Moore, Calvin}, 

TITLE    = {Ergodic equivalence relations, 

cohomology, and von {N}eumann algebras I, II}, 

JOURNAL  = {The Transactions of the American 

Mathematical Society}, 

VOLUME   = {234}, 

YEAR     = {1977}, 

PAGES    = {289-324, 325-359},

}




@article{friedmanbaire,  

AUTHOR   = {Friedman, Harvey}, 

TITLE    = {Borel and Baire reducibility}, 

JOURNAL  = {Fundamenta Mathematicae}, 

VOLUME   = {164}, 

YEAR     = {2000}, 

PAGES    = {333-336},

}



@article{friedman,  

AUTHOR   = {Friedman, Harvey}, 

TITLE    = {On the necessary use of abstract 

set theory}, 

JOURNAL  = {Advances in Mathematics}, 

VOLUME   = {41}, 

YEAR     = {1981}, 

PAGES    = {209-280},

}











@article{friedmanstanley,  

AUTHOR   = {Friedman, Harvey and Stanley, Lee}, 

TITLE    = {A {B}orel reducibility theory for classes 

of countable structures}, 

JOURNAL  = {The Journal of Symbolic Logic}, 

VOLUME   = {54}, 

YEAR     = {1989}, 

PAGES    = {894-914},

}






@book {fuchs,

    AUTHOR = {Fuchs, Lazlo},

     TITLE = {Infinite Abelian Groups},

    SERIES = {Pure and Applied Mathematics},

    VOLUME = {36}, 

 PUBLISHER = {Academic Press},

   ADDRESS = {Cambridge},

      YEAR = {1970},

}



@article{furman,  

AUTHOR   = {Furman, Alexander}, 

TITLE    = {Orbit equivalence rigidity}, 

JOURNAL  = {The Annals of Mathematics}, 

VOLUME   = {150}, 

YEAR     = {1999}, 

PAGES    = {1083-1108},

}





@article{furstenberg, 

AUTHOR   = {Furstenberg, Hillel}, 

TITLE    = {Boundary theory and stochastic 

processes in homogeneous spaces}, 

JOURNAL  = {The Proceedings of Symposium in Pure 

Mathematics}, 

VOLUME   = {26}, 

YEAR     = {1973}, 

PAGES    = {193-229},

}



@article{bogaja,  

AUTHOR   = {Gao, Su and Jackson, Steve}, 

TITLE    = {Hyperfiniteness of abelian group actions}, 

JOURNAL  = {To appear}, 

YEAR     = {$\infty$}, 

}

@article{gaokechris,  

AUTHOR   = {Gao, Su and Kechris, Alexander}, 

TITLE    = {On the classification of {P}olish spaces up 

to isometry}, 

JOURNAL  = {The Memoirs of the American Mathematical 

Society}, 

VOLUME   = {161}, 

YEAR     = {2003}, 

}







@article{gaboriau,  

AUTHOR   = {Gaboriau, Damien}, 

TITLE    = { Cox ut des relations d'equivalence et des groupes}, 

JOURNAL  = {Inventiones Mathematica}, 

VOLUME   = {139}, 

YEAR     = {2000}, 

PAGES    = {41-98},

}







@article{gaboriaupopa,  

AUTHOR   = {Gaboriau, Damien and Popa, Sorin}, 

TITLE    = {An uncountable family of nonorbit 

equivalent actions of $\mathbb{F}_n$}, 

JOURNAL  = {The Journal of the American Mathematical 

Society}, 

VOLUME   = {18}, 

YEAR     = {2005}, 

PAGES    = {547-559},

}





































@article{ghys,  

AUTHOR   = {Ghys, Eitienne}, 

TITLE    = {Groups acting on the circle}, 

JOURNAL  = {Enseignement Mathematique}, 

VOLUME   = {47}, 

YEAR     = {2001}, 

PAGES    = {329-407},

}



@article{glimm,  

AUTHOR   = {Glimm, John}, 

TITLE    = {Type I ${C}^*$-algebras}, 

JOURNAL  = {The Annals of Mathematics}, 

VOLUME   = {73}, 

YEAR     = {1961}, 

PAGES    = {572-612},

}

@article{hakelo,  

AUTHOR   = {Harrington, Leo and Kechris, Alexander 

and Louveau, Alain}, 

TITLE    = {A {G}limm-{E}ffros dichotomy for {B}orel 

equivalence relations}, 

JOURNAL  = {The Journal of the American Mathematical Society}, 

VOLUME   = {3}, 

YEAR     = {1990}, 

PAGES    = {903-928},

}





@article{hamash,  

AUTHOR   = {Harrington, Leo and Marker, David 

and Shelah, Saharon}, 

TITLE    = {Borel orderings}, 

JOURNAL  = {The Transactions of the American 

Mathematical Society}, 

VOLUME   = {310}, 

YEAR     = {1988}, 

PAGES    = {293-302},

}









@article{hjorthproduct,  

AUTHOR   = {Hjorth, Greg}, 

TITLE    = {Non-treeability for product group 

actions}, 

JOURNAL  = {The Israel Journal of Mathematics},

YEAR     = {to appear}, 

}







@article{hjorthdichotomy,  

AUTHOR   = {Hjorth, Greg}, 

TITLE    = {A dichotomy theorem for isomorphism}, 

JOURNAL  = {preprint}, 

YEAR     = {$\infty$},

}







@article{hjorthdye,  

AUTHOR   = {Hjorth, Greg}, 

TITLE    = {A converse to {D}ye's theorem}, 

JOURNAL  = {The Transactions of the American 

Mathematical Society}, 

VOLUME   = {357}, 

YEAR     = {2005}, 

PAGES    = {3083-3103},

}







@incollection{hjorthlogic,  

AUTHOR   = {Hjorth, Greg}, 

TITLE    = {Group actions and countable models}, 

BOOKTITLE = {Logic Colloquium '99}, 

PAGES  = {3-29}, 

PUBLISHER = {Association for Symbolic Logic}, 

ADERESS = {Urbana}, 

YEAR = {2004},

}





















@article{hjorthturbulence,  

AUTHOR   = {Hjorth, Greg}, 

TITLE    = {A dichotomy theorem for turbulence}, 

JOURNAL  = {The Journal of Symbolic Logic}, 

VOLUME   = {67}, 

YEAR     = {2002}, 

PAGES    = {1520-1540},

}





@article{hjorthvaught,  

AUTHOR   = {Hjorth, Greg}, 

TITLE    = {Vaught's conjecture on analytic sets}, 

JOURNAL  = {The Journal of the American Mathematical 
Society}, 

VOLUME   = {14}, 

YEAR     = {2001}, 

PAGES    = {125-143},

}



@book{hjorthclassification,  

AUTHOR = {Hjorth, Greg},

TITLE  = {Classification and orbit equivalence relations}, 

SERIES = {Mathematical Surveys and Monographs}, 

PUBLISHER = {American Mathematical Society}, 

ADDRESS   = {Providence}, 

YEAR ={2000},

}







@article{hjorthorbitcardinals,  

AUTHOR   = {Hjorth,  Greg}, 

TITLE    = {Orbit cardinals: on the effective cardinalities arising as 

quotient spaces of the form ${X}/{G}$ where ${G}$ acts on a {P}olish space ${X}$}, 

JOURNAL  = {The Israel Journal of Mathematics}, 

VOLUME   = {111}, 

YEAR     = {1999}, 

PAGES    = {193-229},

}



@article{hjortheffective,  

AUTHOR  = {Hjorth, Greg},  

TITLE   = {Effective cardinals}, 

JOURNAL = {preprint},

YEAR ={to appear}, 

} 


@article{hjorthborel,

AUTHOR   = {Hjorth, Greg},

TITLE    = {An absoluteness principle for Borel sets},

JOURNAL  = {The Journal of Symbolic Logic},

VOLUME   = {63},

YEAR     = {1998},

PAGES    = {663-693},

}




@article{hjorthdichotomydefinable,  

AUTHOR   = {Hjorth,  Greg}, 

TITLE    = {A dichotomy for the definable universe}, 

JOURNAL  = {The Journal of Symbolic Logic}, 

VOLUME   = {60}, 

YEAR     = {1995}, 

PAGES    = {1199-1207},

}











@book {hjorthkechrisrigidity,

    AUTHOR = {Hjorth, Greg and Kechris, Alexander},

     TITLE = {Rigidity theorems for actions of product groups and 

countable {B}orel equivalence relations},

    SERIES = {The Memoirs of the American Mathematical Society},

 PUBLISHER = {American Mathematical Society},

   ADDRESS = {Providence},

      YEAR = {2005},

}



@article{hjorthkechristhird,  

AUTHOR   = {Hjorth,  Greg and Kechris, Alexander}, 

TITLE    = {Recent developments in the theory of {B}orel reducibility}, 

JOURNAL  = {Fundamenta Mathematicae}, 

VOLUME   = {170}, 

YEAR     = {2001}, 

PAGES    = {21-52},

}


















@article{hjorthkechrisriemann,  

AUTHOR   = {Hjorth,  Greg and Kechris, Alexander}, 

TITLE    = {The complexity of the classification of {R}iemann surfaces and 

complex manifolds}, 

JOURNAL  = {The Illinois Journal of Mathematics}, 

VOLUME   = {44}, 

YEAR     = {2000}, 

PAGES    = {104-137},

}



@article{hjorthkechrismodels,

AUTHOR   = {Hjorth,  Greg and Kechris, Alexander},
 
TITLE    = {Borel equivalence relations and classifications of 
countable models},

JOURNAL  = {The Annals of Pure and Applied Logic},

VOLUME   = {82},

YEAR     = {1996},

PAGES    = {221-272},

}



@article{hjkelo, 

AUTHOR ={Hjorth, Greg and Kechris, Alexander and Louveau, Alain}, 

TITLE ={Borel equivalence relations induced by actions of 
the symmetric group}, 

JOURNAL  = {The Annals of Pure and Applied Logic},

VOLUME   = {92},

YEAR     = {1998},

PAGES    = {63-112},

}




@article{hjorthsolecki,  

AUTHOR   = {Hjorth,  Greg and Solecki, Slawomir}, 

TITLE    = {Vaught's conjecture and the {G}limm-{E}ffros property for {P}olish 

transformation groups}, 

JOURNAL  = {The Transactions of the American Mathematical Society}, 

VOLUME   = {351}, 

YEAR     = {1999}, 

PAGES    = {2623-2641},

}









@article{hrushovski,  

AUTHOR   = {Hrushovski, Ehud}, 

TITLE    = {The {M}anin-{M}umford conjecture and the model theory of difference fields}, 

JOURNAL  = {The Annals of Pure and Applied Logic}, 

VOLUME   = {112}, 

YEAR     = {2001}, 

PAGES    = {43-115},

}









@article{jakelo,  

AUTHOR   = {Jackson, Steve and  Kechris, Alexander and Louveau, Alain}, 

TITLE    = {Countable {B}orel equivalence relations}, 

JOURNAL  = {The Journal of Mathematical Logic}, 

VOLUME   = {2}, 

YEAR     = {2002}, 

PAGES    = {1-80},

}







@article{kanovei,  

AUTHOR   = {Kanovei,  Vladimir}, 

TITLE    = {When is a partial order linearizable}, 

JOURNAL  = {Fundamenta Mathematicae}, 

VOLUME   = {155}, 

YEAR     = {1998}, 

PAGES    = {301-309},

}







@article{kechrisrank2,  

AUTHOR   = {Kechris, Alexander}, 

TITLE    = {On the classification problem for rank 2 torsion-free abelian groups}, 

JOURNAL  = {The Journal of the London Mathematical Society}, 

VOLUME   = {62}, 

YEAR     = {2000}, 

PAGES    = {437-450},

}









@article{kechrissurvey,  

AUTHOR   = {Kechris, Alexander}, 

TITLE    = {New directions in descriptive set theory}, 

JOURNAL  = {The Bulletin of Symbolic Logic}, 

VOLUME   = {5}, 

YEAR     = {1999}, 

PAGES    = {161-174},

}







@article{kechrisideals,  

AUTHOR   = {Kechris, Alexander}, 

TITLE    = {Rigidity properties of {B}orel ideals on the integers}, 

JOURNAL  = {Topology and its Applications}, 

VOLUME   = {85}, 

YEAR     = {1998}, 

PAGES    = {195-205},

}











@book {kechrisclassical,

    AUTHOR = {Kechris, Alexander},

     TITLE = {Classical descriptive set theory},

    SERIES = {Graduate Texts in Mathematics},

 PUBLISHER = {Springer-Verlag},

   ADDRESS = {Berlin},

      YEAR = {1995},

}



@article{kechrislouveau,  

AUTHOR   = {Kechris, Alexander and Louveau, Alain}, 

TITLE    = {The classification of hypersmooth {B}orel equivalence relations}, 

JOURNAL  = {The Journal of the American Mathematical Society}, 

VOLUME   = {10}, 

YEAR     = {1997}, 

PAGES    = {215-242},

}







@book {kechrismiller,

    AUTHOR = {Miller, Benjamin and Kechris, Alexander},

     TITLE = {Topics in orbit equivalence},

    SERIES = {Lecture Notes in Mathematics},

 PUBLISHER = {Springer-Verlag},

   ADDRESS = {Berlin},

      YEAR = {2004},

}



@article{kechrissofronidis,  

AUTHOR   = {Kechris, Alexander and Sofronidis, Nikolaus}, 

TITLE    = {A strong generic ergodicity property of unitary and 

self-adjoint operators}, 

JOURNAL  = {The Journal of Ergodic Theory of Dynamical Systems}, 

VOLUME   = {21}, 

YEAR     = {2001}, 

PAGES    = {193-229},

}







@book {kuratowski,

    AUTHOR = {Kuratowski, Cristoff},

     TITLE = {Espaces {M}etrisables, {E}spaces {C}omplets 2d ed.},

    SERIES = {Monografie Matematyczne},

      NOTE = {French},

PUBLISHER = {Polish Mathematical Society},  

     
   
   ADDRESS = {Warszawa-Wroclaw},

      YEAR = {1948},

}




















@article{louveauvelickovic,  

AUTHOR   = {Louveau, Alain and Velickovic, Boban}, 

TITLE    = {A note on {B}orel equivalence relations}, 

JOURNAL  = {The Proceedings of the American Mathematical Society}, 

VOLUME   = {120}, 

YEAR     = {1994}, 

PAGES    = {255-259},

}



      
@article{mackey,
 
AUTHOR   = {Mackey, George},

TITLE    = {Imprimitivity for represenations of locally cmpact 
groups},

JOURNAL  = {The Proceedings of the National Academy 
of Sciences},

VOLUME   = {35},

YEAR     = {1949},

PAGES    = {537-545},

}



@article{monodshalom,  

AUTHOR   = {Shalom, Nicolas and Shalom, Yehuda}, 

TITLE    = {Orbit equivalence rigidity and bounded cohomolgy}, 

JOURNAL  = {Preprint}, 

YEAR     = {to appear}, 

}





@article{popa,  

AUTHOR   = {Popa, Sorin}, 

TITLE    = {Some rigidity results for non-commutative {B}ernoulli shifts}, 

JOURNAL  = {The Journal of Functional Analysis}, 

VOLUME   = {230}, 

YEAR     = {2006}, 

PAGES    = {273-328},

}







@article{sami,  

AUTHOR   = {Sami, Ramez}, 

TITLE    = {Polish group actions and the {V}aught conjecture}, 

JOURNAL  = {The Transactions of the American Mathematical Society}, 

VOLUME   = {341}, 

YEAR     = {1994}, 

PAGES    = {335-353},

}



 





@book{segal,

    AUTHOR = {Segal, Miri},

     TITLE = {Hyperfinitess},

      NOTE = {PhD. Thesis},

 PUBLISHER = {Hebrew University of Jerusalem}, 

   ADDRESS = {Jerusalem},

      YEAR = {1997},

}





@article{silver,  

AUTHOR   = {Silver, Jack}, 

TITLE    = {Counting the number of equivalence classes of {B}orel 

and coanalytic equivalence relations}, 

JOURNAL  = {The Annals of Mathematical Logic}, 

VOLUME   = {18}, 

YEAR     = {1980}, 

PAGES    = {1-28},

}







@article{solecki,  

AUTHOR   = {Solecki,  Slawomir}, 

TITLE    = {Analytic ideals}, 

JOURNAL  = {The Bulletin in Symbolic Logic}, 

VOLUME   = {2}, 

YEAR     = {1996}, 

PAGES    = {339-348},

}









@article{suwewr,  

AUTHOR   = {Sullivan, Dennis and Weiss, Benjamin and Wright, Mikhail}, 

TITLE    = {Generic dynamics and monotone complete 

$C\sp *$-algebras}, 

JOURNAL  = {The Transactions of the American Mathematical Society}, 

VOLUME   = {295}, 

YEAR     = {1986}, 

PAGES    = {795-809},

}


      
@article{thoma,
 
AUTHOR   = {Thoma, Enver},

TITLE    = {Eine Charakterisierung diskreter 
Gruppen vom type I},

JOURNAL  = {Inventiones mathematique},

VOLUME   = {6},

YEAR     = {1968},

PAGES    = {190-196},

}

      
@article{thomasincreasing,
 
AUTHOR   = {Thomas, Simon},

TITLE    = {The classification problem for torsion-free 
groups of finite rank},

JOURNAL  = {The Journal of the American Mathematical Society},

VOLUME   = {16},

YEAR     = {2003},

PAGES    = {233-258},

}

      
@article{thomassurvey,
 
AUTHOR   = {Thomas, Simon},

TITLE    = {On the complexity of the classification problem for 
torsion-free abelian groups of finite rank},

JOURNAL  = {The Bulletin of Symbolic Logic},

VOLUME   = {7},

YEAR     = {2001},

PAGES    = {329-344},

}

      
@article{thomasvelickovic,
 
AUTHOR   = {Thomas, Simon and Velickovic, Boban},

TITLE    = {On the complexity of the isomorphism 
relation for finitely generated groups},

JOURNAL  = {The Journal of Algebra},

VOLUME   = {217},

YEAR     = {1999},

PAGES    = {352-373},

}






@book{zimmer,

    AUTHOR = {Zimmer, Robert},

     TITLE = {Ergodic theory and semisimple groups},

    SERIES = {Monographs in Mathematics},

 PUBLISHER = {Birkh
â
€
°user Verlag}, 

   ADDRESS = {Basel},

      YEAR = {1984},

}