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\contentsline {chapter}{\numberline {1}Introduction}{1}
\contentsline {section}{\numberline {1.0}Building-blocks}{1}
\contentsline {section}{\numberline {1.1}Structures}{3}
\contentsline {section}{\numberline {1.2}Propositional logic}{5}
\contentsline {section}{\numberline {1.3}Syntax and semantics}{8}
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\contentsline {chapter}{\numberline {2}Propositional model-theory}{11}
\contentsline {section}{\numberline {2.0}Propositional formulas}{11}
\contentsline {section}{\numberline {2.1}Induction}{14}
\contentsline {section}{\numberline {2.2}Recursion}{16}
\contentsline {section}{\numberline {2.3}Syntactic entailment}{20}
\contentsline {section}{\numberline {2.4}Notation}{22}
\contentsline {section}{\numberline {2.5}Theorems}{24}
\contentsline {section}{\numberline {2.6}Logical entailment}{26}
\contentsline {section}{\numberline {2.7}Compactness}{29}
\contentsline {section}{\numberline {2.8}Generalizations}{31}
\contentsline {section}{\numberline {2.9}Completeness}{32}
\contentsline {chapter}{\numberline {3}First-order logic}{35}
\contentsline {section}{\numberline {3.1}Terms}{35}
\contentsline {section}{\numberline {3.2}Formulas}{39}
\contentsline {section}{\numberline {3.3}Logical consequence}{44}
\contentsline {section}{\numberline {3.4}Additional exercises}{47}
\contentsline {chapter}{\numberline {4}Quantifier-elimination}{48}
\contentsline {chapter}{\numberline {5}Relations between structures}{53}
\contentsline {section}{\numberline {5.1}Fundamental definitions}{53}
\contentsline {section}{\numberline {5.2}Additional definitions}{54}
\contentsline {section}{\numberline {5.3}Implications}{55}
\contentsline {section}{\numberline {5.4}Categoricity}{57}
\contentsline {chapter}{\numberline {6}Compactness}{60}
\contentsline {section}{\numberline {6.1}Additional exercises}{66}
\contentsline {chapter}{\numberline {7}Completeness}{67}
\contentsline {section}{\numberline {7.1}Logic in general}{67}
\contentsline {section}{\numberline {7.2}Propositional logic}{69}
\contentsline {section}{\numberline {7.3}First-order logic}{70}
\contentsline {section}{\numberline {7.4}Tautological completeness}{71}
\contentsline {section}{\numberline {7.5}Deductive completeness}{73}
\contentsline {section}{\numberline {7.6}Completeness}{74}
\contentsline {chapter}{\numberline {8}Numbers of countable models}{79}
\contentsline {section}{\numberline {8.1}Three models}{79}
\contentsline {section}{\numberline {8.2}Omitting types}{82}
\contentsline {section}{\numberline {8.3}Prime structures}{84}
\contentsline {section}{\numberline {8.4}Saturated structures}{86}
\contentsline {section}{\numberline {8.5}One model}{87}
\contentsline {section}{\numberline {8.6}Not two models}{88}