Logic in Algebraic Form 1974

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1、LOGICINALGEBRAICFORMTHREELANGUAGESANDTHEORIESWILLIAMCRAIGUniversityo/California,Berkeley,Calif.,U.S.A.I1974NORTH-HOLLANDPUBLISHINGCOMPANY-AMSTERDAM'LONDONAMERICANELSEVIERPUBLISHINGCOMPANY,INC,-NEWYORK

2、reprodllced.storedinaretrieL'olsystem.ortransmitted.itlonyformorbyanymeans.electronic.mechanical.photocopyinJ.:.recordinJ.:orotherwise.withowthepriorpermissionoftheCopyrightowner.Library(!fConJ.:ressCataloJ.:CardNumber72-88292North-Holland/SBNfortheSeries0720422000forthisVolume0720422

3、728AmericonElsevier/SBN044410477IPublishers:North-HollandPublishingCompany-Amsterdam-LondonSoledistributorsj()rtheU,SA,andCanada:AmericanElsevierPublishingCompany.Inc,52VanderbiltAvenueNewYork.N,Y,10017PRINTEDINTHENETHERLANDSTothememoryofmyfatherACKNOWLEDGMENTSloweperhapsmosttothework

4、ofCharlesM.Howard.butamalsoverygreatlyindebtedtoworkoncylindricalgebras.onpolyadicalgebras,andonBooleanalgebraswithoperators.Inaddition,itisapleasuretoacknowledgevaluableconversationswithDanielGallin.BillHanf,LeonHenkin,CharlesHoward,RalphMcKenzie,DonaldMonk,DonPigozzi,AlfredTarskiand

5、RichardThompson.ProfessorsHenkin,MonkandTarskialsokindlymadeavailabletomeadraftoftheirnowpublishedbookoncylindricalgebras.ofwhichImadefreeuseinch.4andinpartsofch.9.Largeportionsofthemanuscript(roughlychs.1-8)werereadwithgreatcarebyRalphSeifert,whospottedmanyerrors,wouldnotpermitvaguen

6、ess,andmadeotherusefulsuggestions.SimilarremarksapplytoDouglasJ.Young,whoreadmostoftheremainingportions.IshouldliketothankPeterEggenbergerforhisfinehelpinpreparingtheindices.Also,IshouldliketorecordmygratitudetoCarrolFluellen,LeslieHausman,JeanneRobinson,DaleOgar,RuthieCephas,andYulia

7、Motofuji,whotypedsuccessiveapproximationswithpatience,accuracy,tasteandjudgment.TheMillerInstituteforBasicResearchinScienceenabledmetodevotetheentireacademicyear1965-1966toresearch.Duringthatyearthisinvestigationgatheredneededmomentum.Mostoftheresultsofch.9andofch.10wereobtained,atlea

8、stinr