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1、一阶模型论的研究及其在代数上的应用摘要First-orderModelTheoryResearchandItsApplicationinAlgebraDuanYanfeng(AppliedMathematics)Abstract:Modeltheoryistodisciplineoneofthemainbranchofmathematicallogic,thetheorytostudytherelationshipbetweentheformallanguagesandtheirinterpretation(model).Modeltheoryori
2、ginatedfromTh.Skolem,formedinthe1950s.Involvedindifferentlogicsystems,modeltheorycanbedividedintofirst-ordermodeltheory,higherordermodeltheory,infinitelengthlanguagemodeltheory,modeltheoryofgeneralizedquantifiers,modalmodeltheory,multi-valuedmodeltheory.Becauseofthemostmaturede
3、velopmentoffirst-orderlogicinmathematicallogic,modeltheoryisthemostabundantonthecontenttothefirst-ordermodel,theapplicationupto.Thispaperdiscussesthefirst-ordermodeltheoryanditsapplicationinalgebra.First,webrieflygivethebasicconceptsandtheoremsofmodeltheory,compactnesstheoreman
4、dtheLSTtheoremisafundamentaltheoreminmodeltheory,modelcompletetheoryhasapplicationstomanymathematicalproblems,themodeltheoreticforcinginthemodeltheoryplaysaveryimportantroleinthefurtherstudyandapplicationofthetheory;Secondly,onthebasisofpreviousresearch,wediscussalimitedpowerto
5、forcetherelationshiptotheexistenceofthestatementandthefullnameofthestatementofspecialsemanticandgrammaticalmeaning,onthisbasis,wediscussthenatureofthefinitemodelconcurrentlysatisfied,wealsodiscussedthenatureoftheinfiniteoftheadmittancemodel;Finally,wefocusontheapplicationofmode
6、ltheoryinalgebra,discussionfocusedontheapplicationofthecompactnesstheoreminthegroup,ringanddomain,giventhedefinitionofanalgebraiccloseddomainandprovedthatanycountabledomaincanexpandtoanumberofalgebraiccloseddomainwiththerelatedtheoryofforce.Keywords:modeltheory;compactnesstheor
7、em;forcing;non-zerofactorringII一阶模型论的研究及其在代数上的应用目录目录第一章绪论......................................................................................................................11.1模型论的起源与发展..........................................................................................
8、.........11.2问题的背景....................................
