Descriptive Set Theory 2009

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1、DESCRIPTIVESETTHEORYYIANNISN.MOSCHOVAKISProfessorofMathematicsUniversityofCalifornia,LosAngelesandEmeritusProfessorofMathematicsUniversityofAthens,Athens,Greeceynm@math.ucla.eduApril8,2009ThisbookisdedicatedtothememoryofmyfatherNicholasagoodandgentlemanCONTENTSPrefacetothesecondedition..............

2、.................................ixPrefacetotheÞrstedition.................................................xiAboutthisbook............................................................xiiiIntroduction...............................................................1Chapter1.Thebasicclassicalnotions.....

3、...............................91A.PerfectPolishspaces..............................................91B.TheBorelpointclassesoffiniteorder...............................131C.Computingwithrelations;closureproperties.......................181D.Parametrizationandhierarchytheorems.........................

4、...261E.Theprojectivesets................................................291F.Countableoperations............................................331G.Borelfunctionsandisomorphisms.................................371H.Historicalandotherremarks......................................46Chapter2.κ-Suslinandë-

5、Borel..........................................492A.TheCantor-BendixsonTheorem...................................502B.κ-Suslinsets......................................................512C.TreesandthePerfectSetTheorem.................................572D.Wellfoundedtrees.............................

6、....................622E.TheSuslinTheorem...............................................652F.Inductiveanalysisofprojectionsoftrees............................702G.TheKunen-MartinTheorem......................................742H.Categoryandmeasure.............................................792I.Hist

7、oricalremarks................................................85Chapter3.Basicnotionsoftheeffectivetheory..........................873A.Recursivefunctionsontheintegers.................................89