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1、LectureNotesinMathematics1888Editors:J.-M.Morel,CachanF.Takens,GroningenB.Teissier,ParisJ.vanderHoevenTransseriesandRealDifferentialAlgebraABCAuthorJorisvanderHoevenDépartementdeMathématiques,CNRSUniversitéParis-SudBâtiment42591405OrsayCXFrancee-mail:joris@texmacs.
2、orgLibraryofCongressControlNumber:2006930997MathematicsSubjectClassification(2000):34E13,03C65,68w30,34M35,13H05ISSNprintedition:0075-8434ISSNelectronicedition:1617-9692ISBN-103-540-35590-1SpringerBerlinHeidelbergNewYorkISBN-13978-3-540-35590-8SpringerBerlinHeidelbe
3、rgNewYorkDOI10.1007/3-540-35590-1Thisworkissubjecttocopyright.Allrightsarereserved,whetherthewholeorpartofthematerialisconcerned,specificallytherightsoftranslation,reprinting,reuseofillustrations,recitation,broadcasting,reproductiononmicrofilmorinanyotherway,andstora
4、geindatabanks.DuplicationofthispublicationorpartsthereofispermittedonlyundertheprovisionsoftheGermanCopyrightLawofSeptember9,1965,initscurrentversion,andpermissionforusemustalwaysbeobtainedfromSpringer.ViolationsareliableforprosecutionundertheGermanCopyrightLaw.Spr
5、ingerisapartofSpringerScience+BusinessMediaspringer.comcSpringer-VerlagBerlinHeidelberg2006Theuseofgeneraldescriptivenames,registerednames,trademarks,etc.inthispublicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfromtherelevantprotect
6、ivelawsandregulationsandthereforefreeforgeneraluse.TypesettingbytheauthorandSPiusingaSpringerLATEXpackageCoverdesign:WMXDesignGmbH,HeidelbergPrintedonacid-freepaperSPIN:11771975VA41/3100/SPi543210TableofContentsForeword......................................XIIntrod
7、uction....................................1Thefieldwithnoescape..........................1Historicalperspectives............................3Outlineofthecontents...........................7Notations....................................101Orderings....................
8、...............111.1Quasi-orderings.............................121.2Ordinalnumbers............................151.3Well-quasi-orderings.........
