Model Theory, Third Edition (Dover Books on Mathematics)

Modeltheorydealswithabranchofmathematicallogicshowingconnectionsbetweenaformallanguageanditsinterpretationsormodels.Thisisthefirstandmostsuccessfultextbookinlogicalmodeltheory.Extensivelyupdatedandcorrectedin1990toaccommodatedevelopmentsinmodeltheoreticmethods—includingclassificationtheoryandnonstandardanalysis—thethirdeditionaddedentirelynewsections,exercises,andreferences.Eachchapterintroducesanindividualmethodanddiscussesspecificapplications.Basicmethodsofconstructingmodelsincludeconstants,elementarychains,Skolemfunctions,indiscernibles,ultraproducts,andspecialmodels.Thefinalchapterspresentmoreadvancedtopicsthatfeatureacombinationofseveralmethods.Thisclassictreatmentcoversmostaspectsoffirst-ordermodeltheoryandmanyofitsapplicationstoalgebraandsettheory.